Well, most often you can't choose.
Often you need the train to get from one city to another
and then the bus to get to your final destination that might be a small village.
Even though private bus companies try to get into the market, the trains between cities are at the moment still way more frequent and reliable.
In particular for you first two journeys, to Montreaux and Lucerne, I would take the train.
As far as I know, there is not even a bus connection available, and even if there would be one, it wouldn't be faster than the direct train that takes 1 hour to Montreaux, respectively three hours to Lucerne, without the need of changing trains.
Check out sbb.ch for up to date time tables.
In any case, think about buying a half fare card .
You pay 150 CHF and then every ticket that you buy within a year
costs only half its original price.
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Last year I was also checking Swiss bus tickets online but couldn't find anything better.
Switzerland has a very pristine rail network and maybe that is a reason Swiss government just focuses on rail network rather than buses.
I visited Switzerland last year and bought Swiss individual super saver tickets and found really cheaper as a tourist.
Here is the link for that website: http://www.sbb.ch/en/travelcards-and-tickets/tickets-for-switzerland/supersaver-tickets.html
And you have just mentioned that you have currently moved to Switzerland and
you have a longer stay there.
The half-fare travel card is the best option for your travel within Switzerland.
you could get all the required information from this website: http://www.sbb.ch/en/travelcards-and-tickets/railpasses/half-fare-travelcard.html
Also the route just mentioned Geneva-Montreux-Lucern is really worth to travel through Train.
It is a spectacular scenery specially from Montreux to Lucern
There is also a website where you can find buses fares and connections in Switzerland: https://www.postauto.ch/en
travel.stackexchange.com/users/43993/Ali Awan
You can't take a bus between major towns/cities in Switzerland, as buses are not allowed to compete with the train system.
In der Schweiz dürfen Fernbusse Passagiere nur über die Grenze, aber nicht innerhalb der Schweiz von einem
Ort zum anderen transportieren.
which translates to In Switzerland, long-distance buses can only transport passengers over the border, but not from one place to another within Switzerland
The Post Auto buses supplement and extend the train network, but don't act as competition to the existing train routes.
International bus routes starting in Switzerland exist, and are an option for visiting cities in neighbouring countries, but by law you can't get off the bus until you cross the border.
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If you are open to other options, consider car sharing.
It doesn't have to be your car.
You can look up on any version of blablacar (linked to the UK one for english) and find really cheap rides to big cities of Switzerland.
If you don't find a ride to where you want to go, you can rent a car and then get some other passengers to share the ride and split the cost.
While car renting in Switzerland is quite expensive, since you live in Geneva you can rent the car from neighbouring France, which is considerably cheaper.
Keep in mind there is a constant stream of new people in Geneva and everyone wants to travel for cheap, so it's easy to find fellow passengers.
Just post in the facebok groups of the area.
travel.stackexchange.com/users/52244/Ciprian Tomoiagă
In addition to the existing advice (especially about the half-fare travelcard), if you're going to really use public transport a lot (for at least 4 months), you may also want to see whether it's worth it to get the GA (Generalabonnement) travelcard .
If you have the half-fare travelcard, it's also possible to get the 1-day travelpass .
Note that it's quite common for municipalities to offer those 1-day travelpasses for a discounted price to their residents, but they are available in limited quantities and only for the local residents.
( see here for Geneva )
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As for Geneva bus system (TPG)- if you use the bus to go to work at least 3 times a week - get a monthly abonnement for 70 CHF.
I work as a freelancer, so I don't commune anywhere - for me just getting a full fare for 3 chf from time to time is better.
For train system:there are also supersaver tickets http://www.sbb.ch/en/travelcards-and-tickets/tickets-for-switzerland/supersaver-tickets.html - discounted tickets but time and date are fixed, also they are non-refundable.
You might also benefit from Carte journaliere (full day pass for all means of transport in whole Switzerland for 42 CHF) http://www.ville-geneve.ch/demarches-administratives/mobilite/carte-journaliere-cff/ (purchase in advance)
Count
what works for you better - sometimes just paying full price is cheaper than getting an abonnement.
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I have very good memories of using one of the Swiss rail websites , but I can not find anything on long distance buses, Rome2Rio does not give them, google does not give them.
Buses in Switzerland do the short distances from the railway station towns to the villages, sure.
But I can not find long distance buses online.
So the answer to your guestion is: Trains are likely the cheapest option for long distance travel where you do not want to use a car, as buses do not connect places far apart.
When booking early, do check flights and travels via other countries.
Which train and how much it costs you can find on any of the rail sites that give prices for Switzerland.
travel.stackexchange.com/users/27650/Willeke
Most of Swiss residents who use public transport have the half price card ("halbtax") that reduces the price as much as twice.
It is valid in all trains and most of the buses.
As you have the living address in Switzerland, I would strongly recommend to obtain such a card first thing to do.
It may look expensive but will pay itself in a first few journeys.
Also, when using the city transportation system, be aware that tickets are valid in all zones indicated on the ticket, regardless of the travelling direction or anything the like.
These systems cover a huge areas (for instance, Zurich system also covers all Winterthur and good piece of land around).
You can buy 24 hour ticket for all zones and spend all day on the way in any direction.
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My husband and I recently moved to Geneva. We both will be working and sometime travelling within Switzerland for sightseeing on weekends. We will be mostly visiting different parts but for only two nights at a time, so obviously we don't need a Swiss Pass. Our first plan is to visit Montreux and Lucerne.    What is the cheaper option, bus or train?
Train and bus costs in Switzerland
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<trains><budget><buses><switzerland>
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travel.stackexchange.com/users/52230/Naureen Khan
Trains are way more frequent and reliable than buses in Switzerland, and intercity national buses are not permitted in the country. You could consider buying a supersaver ticket, Carte journaliere (full day pass for all means of transport in whole Switzerland for 42 CHF) or half-fare travelcard, and you can compare prices on any of the rail sites. Another option is to try car sharing, e.g. with blablacar. Travelling by train is definitely the preferred means of transport between cities in Switzerland and several type of card are available for travellers, for example the half-fare card. Buses are not available between cities as they are not allowed to compete with the train system. Alternative options include flying and car sharing.
Train is definitely the major means of transport between cities in Switzerland.  The system is very good and all schedules and prices are available on railway websites. Bus routes are not allowed to compete with the train system so there are no connectionc between major cities. There are international bus routes starting in Switzerland. There are a number of special cards for travellers, including the half-fare card. There are other option for travelling in Switzerland including flying and car sharing.