Two things to keep in mind that many people aren't ware of related to strollers at Disney.
In the Parks
IF the stroller will not roll on the ground through the stroller gates located between the turnstiles, then technically it is too large for the park. In this case it is at the CM's discretion to assist in lifting the stroller over the gates, or sending you to Stroller rental for one that is appropriately sized to use in the park while yours is stored until the end of the day.
Additionally, Cast members often times find it necessary to move strollers for a variety of reasons, but mostly to keep them from blocking paths in case of emergency. Locking it to an inanimate object, could do more harm than good. If the need arises to move the stroller for safety, and they cannot locate you, I am sure the appropriate staff member will be called to assist in removing it from the object.
Strollers and Bus Transportation
Under no circumstances, are strollers allowed to be open with or without a child in them while on a Disney Bus. Also, someone from the party must hold on to the stroller for the entire trip. It cannot sit unattended in a seat or on a ledge as they can become projectiles in a quick stop or accident. These are a violation of Federal Regulations and can get the bus driver in serious trouble.
Also, it is at the drivers discretion, as to whether or not the rear doors will be opened in order to accomodate bringing your stroller on board. As a rule of thumb, plan on the front door and then ask nicely about the rear door if it is a larger stroller only.
Their answer will depend on the situation. If there is a large crowd waiting to board the bus, they may not open the rear door because they quicly lose control of entering and exiting safety.