We always took a stroller that was better than an umbrella stroller but in the lightweight cateogry, with these features:
1) Bag storage
2) cup holder (hard to drive and hold a drink)
3) sun shade
4) back that lowers for napping
5) Seatbelt
Don't overpack, and put your stuff in a bag that drops into the bag storage area. This way you can pull the bag out fast, fold the stroller and get on the bus. I see so many families that can't fold their stroller becuase they have so much junk crammed into the storage basket.
Don't hang a bag on the handle, you will tip over the stroller a lot.
Use the seatbelt, even for older toddlers. This prevents them from suddenly getting up while you are rolling... which usually plants them face down on pavement.