I've been dating this guy for 2 months now. We are both mature adults. I'm a bit old fashioned and believe the guy should always do the asking. But now I wonder if he wants me to ask him out at times also? What it be a good sign for him? I've never declined when he's asked me out.

Well if you've been dating for two months there's nothing against you suggesting activities.

Ask the guy out say for some activity.. it never hurts. Who knows , he may just b asking himself " should I ask her out?"

Yes! It's perfectly fine for a woman to ask a guy out.

If you've been dating for two months, then I feel that things should slowly progress to being 50-50. A guy can't always ask the girl out, it gets tiring.

Yes. You aren't doing your fair share of the work if you don't suggest anything and ask him out. Don't be passive and make him guess what you'd like to do!