Hi Diane,
Welcome back to the Disney Parks Moms Panel!
Your question brought a smile to my face because it made me remember my little guy's first visit to Walt Disney World Resort when he was 5 months old. At that time, he was still in his "bucket" (i.e. portable car seat) that would attach to his stroller. We were able to take the bucket with us on
Disney Transportation without any problems, although it was a bit bulky on a crowded bus when combined with the stroller.
If I understand your question correctly, you've got a pram attachment for your stroller (kind of like a bassinet). While I don't think the pram wouldn't necessarily need to be collapsed, I do worry that it might be a bit bulky, especially on a crowded bus (which could lead the driver to ask you to collapse it for safety reasons). Instead, I would highly recommend "baby wearing" (i.e. using a baby carrier such as a Baby Bjorn or a wrap/sling). After a day or two of trying to wrangle our stroller and bucket, I started wearing my little guy and it was so much easier! I have some wonderful memories of having him snuggled up to me, sleeping peacefully as we walked around the Parks.
Please note that you won't need to collapse your stroller (or pram) if you take the monorail, a definite plus for Guests with little ones who have chosen to stay in a Walt Disney World Resort Hotel located along the monorail line.
Finally, please don't forget to visit the
Baby Care Centers for a much-needed respite from the sun and crowds during your visit.
Please don't hesitate to come back and visit us! I love helping Guests plan the perfect vacation with their itty bitty babies.
Have a Magical Day,
Lynne