Hm...well, technically, since she had said no, she didn't want to 'go out' with you, she can't complain if you go on a date with someone else. I can't help but think, however, that you should perhaps have discussed the rules of your arrangement more carefully. I've never liked the whole 'dating but not exclusive' model, because to me it just unnecessarily confuses things.
The fact that you feel bad about it suggests that on some level, you felt more attached to this girl than your relationship status suggested.
If you still want to go out with her, I would have a chat about where things stand, and set out some rules. Remember what happened on Friends when Ross and Rachel were on a 'break' but hadn't set boundaries for it? A lot of whinging and recrimination, that's what. If she doesn't want to know, you'll just have to cut your losses, and learn the lesson for next time (if there is one).
The fact that you feel bad about it suggests that on some level, you felt more attached to this girl than your relationship status suggested.
If you still want to go out with her, I would have a chat about where things stand, and set out some rules. Remember what happened on Friends when Ross and Rachel were on a 'break' but hadn't set boundaries for it? A lot of whinging and recrimination, that's what. If she doesn't want to know, you'll just have to cut your losses, and learn the lesson for next time (if there is one).