I can't imagine they would let you take your own bike ad trainer in, but, hey, it would be cool if you could and can't hurt to ask. Wouldn't bother me while I am leading a class if someone did that, but again, I know the "Y" where I spin wouldn't allow it. I usually ride a class at home first on my trainer before I take it to the spin class. Riding your own bike is just better but it can get lonely indoors.
Time is a companion that goes with us on a journey. It reminds us to cherish each moment, because it will never come again. What we leave behind is not as important as how we have lived." Captain Jean Luc Picard