In a letter with Bexhill and Battle MP Huw Merriman, the Hastings and Rye MP said constituents would otherwise face higher costs and longer journeys.
They also expressed disappointment about the lack of reinstatement of the emergency timetable across Sussex.
RMT members are due to stage a 48-hour strike on 7 and 8 September.
The rail union is fighting moves to turn conductors on Southern into "on-board supervisors", with drivers taking over responsibility for opening and closing carriage doors.
The union has said it has concerns over safety and job cuts, but the company began imposing the changes earlier in August.
In their letter to the managing director of Southern rail, Charles Horton, the MPs said the industrial action was "regretted in circumstances where the RMT have been offered guarantees on jobs and pay".
Ms Rudd and Mr Merriman said bus replacement services would "minimise the impact" of next week's strike.
"A failure to provide a bus replacement service sends out the signal that constituents closer to the coast are not treated with the same sense of urgency as those closer to London.
"This has already been exacerbated by the news this week that certain services which had been subject to the temporary timetable have been returned to normal in south London and Surrey but not in Sussex," they said.
The MPs went on to point out that their constituents, unlike other parts of the network, would not be able "to enjoy the benefits of the new driver-operated trains", and were suffering "more detriment than others".
Mr Merriman later told BBC South East that he had received "a communication" from Southern saying the timetable to the coastal routes in Sussex would be reinstated "within weeks".
The operator introduced a reduced service in July after months of delays and cancellations, which it blamed on "unprecedented" staff sickness.
Home Secretary Amber Rudd has written to Southern rail calling for "adequate" bus replacement services to be provided in Sussex during the next RMT strike.