That's no lie. You should probably assume that some of your clients could find out as well. But that might not be a tragedy in and of itself. Depends on the type of business, I suppose. I happen to work in a field that is pretty tolerant of all different types, but I know that doesn't apply to everyone.
I guess what I'm saying is if you tell her, in a way, you kind of have to look at it like you are telling everyone. If you're cool with that, then okay. If you're not, you might want to wait to open that door.
I trust my girlfriend with my life, but when I told her I knew that potentially I was telling everyone. It didn't work out that way, but you have to cover all your bases.