I would 150% have the procedure done with a bulldog specialist. The breed is very different from others in regards to going under. You want someone who knows the breed. You said you're in the Woodlands right? Our vet specializes in bulldogs, and they have performed surgery on Tyson as well. I know its not super close for you -- but its not far I would totally make the trip for this procedure knowing she's in good hands. We have lots of Houston members who go there as well Brittmore Animal Hospital. They are located off the Beltway & I-10. Brittmoore Animal Hospital - Home I know that Todd @Marine91, David @Davidh @1Chumly @sunkissedpr1ncs are a few off hand that can vouch for them as well.
All the docs there are great, we've been to Dr. Dikeman, our usual go to is Dr. Chellappan (she has a frenchie), and Dr. Burbridge is the one who performed Tyson's surgery. I cannot rave enough about them. Other than the spay, hopefully you don't need anything else major, but if you ever have something "bulldog specific" I would go there.
In terms of walking, its something you just have to work on everyday. LOL It will slowly get better. I would try a harness instead of a leash, takes pressure off the neck, and it give you much more control. Also, bust out the treats.... small ones so you can reward her walking, or get her to move when she's still. Eventually she'll catch on! She's precious!!! Can't get enough pictures!