I would like to ask for it as soon as possible, but don't know how to approach my new boss in a professional and non-awkward manner.
You are seriously overthinking this one.
Something like "Hey boss.
I noticed that the women's bathroom doesn't have a sanitary bin.
Could we get one?
" would be fine.
If you would find that too embarrassing to suggest in person, make the suggestion via email.
You might even offer to pick one up and get reimbursed.
And as @Martijn suggests, you could even find one and order it online.
In small offices it wouldn't be unusual at all for folks to order things then get reimbursed.
It's understandable, but try not to be nervous about this sort of thing.
We've all gone through a "first job" experience.
It gets much easier with time and practice.
workplace.stackexchange.com/users/7777/Joe Strazzere
Just very casually.
"
Hey, I noticed that the trash bin in the ladies room is gone.
Who do I need to see to replace it".
Don't borrow trouble, just go in assuming that it's a normal, everyday thing because it is.
Update due to edit: Still make it "Hey, I noticed that we don't have a sanitary bin in the ladies room, who do I need to see to get one put in there?
I just don't want medical waste put in with the regular trash"
workplace.stackexchange.com/users/46894/Old_Lamplighter
If you're uncomfortable talking about it face-to-face, email might be a better alternative.
You don't need to go into too much detail.
Something like this: Our ladies' room is missing a bin for sanitary products.
Can we order one?
Martijn made the excellent recommendation in his comment to do an internet search for one - you could include that in your email as well so that there is no confusion at all.
workplace.stackexchange.com/users/75608/Mike Harris
If you still feel too uncomfortable to ask directly, or you aren't familiar enough with the laws regarding sanitary bins in your region, consider enlisting the help of the older women in the office.
You may find they'll take care of the problem for you.
workplace.stackexchange.com/users/10512/Adam Davis
It is not stated what country you are in, but check if your company has a safety committee or health committee, or both.
In Ontario, Canada, employers of a certain size are required to have a "Joint Health and Safety Committee" (JHSC) with a mandate to identify health & safety issues, receive them from employees, and make recommendations to the company.
If you decide not to pursue this with your immediate supervisor, you may be able to report the missing bin to the JHSC or equivalent, and they'll be able to request that the company supply one.
workplace.stackexchange.com/users/26934/tar
It’s awkward to ask your boss for things like this.
So don’t.
Ask the person who cleans the restrooms at night.
The maintenance of the restrooms might not even be your company’s responsibility.
Suggested wording:
“the ladies’ restroom needs a sanitary disposal bin; can you please take care of that?
Thanks!”
(Among other things, the person who will be dealing with the mess if a flushed pad blocks the plumbing is a lot less likely to be embarrassed by the request.)
workplace.stackexchange.com/users/29320/arp
I've recently started working in a small business (10-15 employees), and noticed that the women's bathroom lacks a sanitary bin. Since the team is mostly male, and the only two other female employees are both over 50, it was probably not a problem before.  How should I ask my (male) boss for a sanitary bin in the women's bathroom in a professional and,  ideally , non-awkward manner?
How to ask a male boss for a sanitary bin in the women's bathroom?
workplace.stackexchange.com
<communication><new-job><women><bathroom>
workplace.stackexchange.com/questions/99937
workplace.stackexchange.com/users/77598/GreenOwl
Address is casually over email if you are embarrassed to discuss it in person. If you feel uncomfortable making this request face-to-face, consider writing them an e-mail. Keep it casual and don't go into too much detail - there's no need.
If you feel uncomfortable making this request face-to-face, consider writing them an e-mail. There is no need to be overly formal or go into too much detail.