The bank change command is controller 0, optionally followed by its LSB partner, controller 32. The change should not take effect until a program change is received, so the messges sent should be:
No synthesizers have enough banks to need both MSB and LSB, so a few expect the number in the MSB and don't need an LSB. Others demand an MSB of 0, with the bank number in the LSB. They are supposed to wait for the program change before changing sounds, but a few change instantly upon receipt of the bank change.
The actual bank numbers are not always what you would expect. Many machines use 0 1 2.. etc, but the Roland JD 990 numbers its two banks 80 and 81. There is also the same confusion about starting with 0 or 1 that we have on the program numbers. Some instruments also use bank changes to switch between performance and voice play mode.
Many instruments may have some other way of dealing with bank changes. For instance, on Emu samplers there is a "magic preset number". When this is received as a program change, nothing happens, but the next program change is interpreted as a bank to load off disk.