Yes. Correct. call BME.begin() every time and the subroutine only at the beginning.
And you are also correct about the library. I use the "blue" lib, from Sparkfun. As i can recall correct (it's been over a year since I built the damn thing) I have tried both, and found the Sparkfun more stable.
And you CAN switch off power for this module, but after conversion it goes to sleep and uses less than 1uA. Hardly worth the effort, because the current can find a way over the data lines, and that's a pain in the behind to solve (I tried!).