We've been fine with a stroller on the buses. But I think it helps if - A.) you have a relatively lightweight and compact stroller (Maclaren - well worth the money) I wouldn't want to take one of those huge 50lb strollers to the mall, let alone to WDW. Going back and forth with one of those would be a PAIN.
It's worth it to have a stroller that folds relatively easily.
and B.) you have a system. By the end of our last trip, we had it down to a science! Mind, we had a group system (one person took the children, another took the stuff, another took the stroller). I think it's easier if you can take the stroller all the way to the bus stop at each park and have it to get around the resort (unless you're on the fourth floor on the AB side of POR

- no elevators there! "Rustic" is not so cute after a day in WDW!)
In terms of bringing items, we also had a system. We put the necessary items in a compact backpack (Jansport half pint
http://www.jansport.com/js_product_detail.php?cid=20&pid=TDH6 ) -or even minimize the valuables down to items that will fit in one's pockets. It helps of DH wears cargo type shorts with lots of pockets!
Then the water bottles/baby bottles/diapers/wipes (non-valuables) went in gallon ziploc bags each day.
Then we dumped the ziploc bags into a Disney shopping bag...and everyone carried any sweaters or anything they had.
The Disney plastic shopping bag is good cause it has handles, and you don't care if you lose it. Boy, are those things sturdy!
When you get off the bus, dump the contents of the Disney bag (ziplocs) into the bottom of the stroller. Tuck the Disnety bag underneath. Security then won't ask to 'see inside' your stroller bottom, because they can see everything already. So minimal unpacking at teh security checkpoint - everyone loves that!
After security, you can maybe add your sweaters to the bottom of the stroller, depending on the size of your stroller basket.
This all sounds a little complicated, but actually it can be done really fast. Not only that, but packing up for each day is a snap in the morning. Any undrunk water can go right into the fridge, The diaper/wipes ziploc can be easily repacked, etc. And ziplocs have 101 uses! We don't like to carry around lots of 'stuff' - we really like to minimize, but they have come in handy any number of times - like when a diaper leaks...