This is such a personal preference sort of question, but here is my 2 cents. First, don't bother buying a new one just for Disney. These boards are an awesome wealth of info, but sometimes it makes you think you must have this and do that when you go to Disney. ( I catch myself thinking that way a lot).
If your daughter is more comfortable in or you are more comfortable pushing the regular stroller--I say take it. Yes, strollers on the bus aren't the most fun, but it is not THAT bad (I have done it with a Joovy Caboose and survived). The comfort factor of both the child & parent who has to push it in the parks all day far outweighs the bus inconvenience factor.
The umbrella could work too, but we don't know what type of umbrella you have. I would not take a cheapie umbrella (think
walmart for $15). They are good for quick rides...which Disney is not.
The "medium" priced umbrellas are a little better and I might consider taking one if my daughter was comfortable in it, if it was comfortable for me to push for a mile or two and I was not going to be lugging a backpack full of crap nor buying a ton of things in the parks (which would end up hanging on the handles). I am thinking some Jeep or Kolcraft models here.
The higher end umbrellas are awesome, but I woudn't pay $100+ for another umbrella just for one specific vacation. (these would be your maclarens, inglesina, britax)
just my opinion of course...