Can you use the bats form or something to get through those pesky doors inside of caves that refuse to grant entry to Vampire Lords? What about mist form? I think it's really annoying having to revert and retransform. I just want to stay in my true form, darn it!

Yes sometimes but not always, and you are not supposed to stay in vampire lord form all the time, that is why there are disadvantages.

I tried but I don't think it works with the bats.

Yep your character is still the same size just in a different form.