How do you approach a woman without it appearing like you're "hitting" on her?

I am a very sociable person. I have no problems with talking with women, but, sometimes women think I'm "hitting" on them. I'm interested in a relationship and I'm not a "player." I've had bad experiences (at times) where I strike up a conversion with a woman and I ask her if she'd like to get together sometime, next thing I know she's telling everyone that I was "hitting" on her. A very nice woman came into my office the other day, she was very personable and we seemed to be getting along with each other. I wanted to ask her out for a cup of coffee, but, I've had bad experiences in the past. The last thing I would want is for a client to start complaining about me because I want to make a new friend. She left and the chance of ever seeing her again is slim to none. So my question is: How do I approach a woman without it appearing like I'm "hitting" on her?