I definitely recommend bringing your own. Too expensive to rent. And nice to have on the way to the bus, etc. - especially with 2 young ones.
If you have at least 2 adults...dh and I got the whole bus thing down to a science:
1) put an empty shopping bag (think 99 cent grocery store reusable) on the bottom of your stoller at the start of the day. Put everything you store here on top of it.
2) When going back to the bus in the afternoon/evening, keep kids in it as long as possible...when you see the bus coming is when to hop into action.
3) get both kids out of stroller and grab the backpack/bag out and then take the shopping bag and put any incidentals that have ended up in the bottom of the stroller into it (half empty water bottles, wet socks, popcorn buckets, etc.) - it is MUCH easier to throw all these things into one bag to keep your hands available for the kids.
4) I would take both kids hands (when possible - if younger wasn't sleeping) and walk on. DH would go in back door (when it was opened, isn't always) and stand with the stroller against one of the poles near the back door. He would prop it up against the pole and stand against it.
5) I sit with one kid on lap and one next to me.
6) At exit point - DH hops out quick and has stoller setup ready for kids to jump into when we get off the bus.
Never had a problem with it. If it is only one adult, IMO, is the only time it makes it much more difficult. Also if both kids fall asleep on the bus - but the driver usually lets dh get back on bus quick after he has stroller setup to grab one sleeping kid while I carry the other one out.