There will be Thruway bus from Bakersfield to Lancaster. The luggage space in the passenger compartment is very limited, and most items will go in the luggage hold under the bus. I really wonder if they'll allow that bag in the luggage hold.
If it fits in the overhead or can be carried in the seat, I don't see what the problem would be.
That is the big "if". The amount of room available inside the passenger compartment of the bus is much more limited than onboard the train. Room in the overhead is very limited. "Carried in a seat" implies that the trash bag full of clothes is occupying a seat, which is problematic if the bus is full, so I would amend that to "carry in your lap". In my own experience, luggage I carry onboard a train goes in the luggage compartment in on a bus, and I only carry relatively small personal items (CPAP machine, daypack) with me on a bus.
If it was train only and no bus involved, I would say it probably would not be an issue.
I am envisioning one of the relatively big, black trash bags, so it really all depends on size.