How to handle kids asking about new girlfriend?

Started dating someone about 4 months ago and it's getting serious. My oldest asked yesterday if she's my girlfriend. I didn't want to lie but I also don't want to introduce her to the kids yet. My ex is already making comments about me 'parading women around.' How do other guys handle this? What's the right age to introduce kids to a new partner? I share 50/50 custody if that matters.