I have a generic one and I can leave it on, I just have to unhook the front two bungee straps that hook into the soft top latches. Otherwise it's there ready to go and takes 2 seconds to hook the bungees up.
I'm assuming they probably hook into the same holes or similarly.
Yes you can keep the Ford Bimini top installed with the factory or the Bestop. Just have to unhook the corner straps and the 2 center hooks. Quick and easy! I had it installed before I picked my Bronco up by the dealer. Then later I replaced the factory soft top with the Trek top by Bestop.