Hi Danny
Yes you should be able to remove the bolts to fit the stabiliser bracket. Especially as they won't have had to "corrode" in!!! You could even ask the towbar fitter not to do the bolts up too tight so that you can remover them more easily, as long as you're not towing before you tighten them up of course!!!!
On the other hand if you can get the bracket to the towbar fitter when he fits it it would save you having to bother further. They do, understably, torque up the bolts very tight!!! Regarding the extra length of the bolts I've just popped out and measured the thickness of my stabiliser bracket, although mine's NOT Bulldog, I'm sure it would be similar, and mine is 1cm thick. The thickness of the protector is neglible, just sheet steel and then I,also, have a Witter towbar cycle carrier bracket which is 1 cm thick. My towbar fitter, my towbar is a Witter, used 10cm bolts and gives a LOT of thread to spare. If you are fitting the bracket later you need to make sure that the bolts the towbar fitter are not only long enough but not too long either which would prevent them from fitting between the ball and the front of the towbar itself, eg, if I took off cycle carrier and stabiliser brackets I would have to change to shorter bolts.
Incidentally, just to confuse you further!!! LOL, are you having 13 pin or twin electrics fitted to the towbar. I had 13 pin fitted on the car and changed my caravan twin sockets to a single 13 pin. That electrical system is MUCH more reliable as it locks into place and avoids problems like shorting from badly fitting pins and might be worth considering. If you do go for the 13 pin system on the car stress to the towbar fitter that you want the right thickness of cable used - some are too thin.
Regards
Tim