Does turning a phone on and off deplete battery life?
Leaving the phone on but disabling it from the telephone network (airplane mode) would ensure that the battery drain from it being interrogated by the cell network is minimized. Once on, I would suspect that after a minute or so (I'm thinking android at this point) all the apps you might normally have activated will be loaded and the phone can go into light standby. How long does a bus or train journey last? How much lower is standby power than normal power? How much power is re-used on turning the phone back on just to load the apps and power up the screen?

My phone currently tells me this about my battery usage: -


Screen 33%
Cell standby 22%
Phone idle 20%
Wifi 19%
Google play services (whatever that is) 6%


I don't have bluetooth enabled so that isn't draining anything.

Do some research and find out what the power consumption proportions are for each mode and I would suspect that if the bus journey is less than 15 minutes (gut feeling) it might be more economical to leave it switched on and doing nothing.