I had my personal wc for our recent trip. We didn't use the bus much (we drove except for the MK and then also had to take the Fort Wilderness bus as we went to the Hoop De Doo). I guess I could have hopped up and had my dh fold the wc, but there I was, sitting in it waiting for the bus. When it arrived, taking the path of least resistance, I simply stayed in my wc. The driver did not ask if I wanted to transfer and I didn't volunteer to do so (when in an
ECV, they always asked and when I said I could transfer, they had me do so). They loaded me in with the lift and then strapped me in with a big seatbelt and strapped my wc in with FOUR different belts. Like Sue, I believe that a folded wc would be boarded at the rear. I assume that they would strap it in with the standard collection of tie down straps so whether she sits in it or not, it would take up the wheelchair spot (eg a bench worth of seats). I have no basis to say this, but I can't imagine they would let it stay folded and not tied down. What if the bus stopped suddenly and it rolled and hit someone?
Like Cheshire Figment says, if you are going with a wc, it's better to rent offsite. The resort wcs are variable in terms of condition and availability. Before I found this board and learned about offsite rentals, I had to wait almost 2 days for my resort to borrow one from another resort one time as they were out. The offsite ones are also far more comfortable in terms of back support and adjustability of footrests plus the better condition makes them easier to push. Note that the Swan and Dolphin do not have wcs to borrow.
I'd also think about an ECV. If your MIL wants to do that, she will absolutely want to rent offsite.
Have a fun trip!

Cupcake
p.s. A big THANK YOU to Sue and Figaro for the helpful posts re taking my wc on a plane. It worked like a charm! (armed with the great info, we were able to stash it in the first class closet both ways).