Please try to put the best interpretation on this -- not the worst. She may not have phrased it very gracefully, but she was on the spot; you had just asked her point-blank if you could come along on a previously arranged outing with another person you don't know, and she was on the spot to provide you an answer -- that second. Can you see how she might have put it less than ideally?
Also, consider this: There are ton of reasons she could have done this and none are about you or whether she likes you.
This other friend of hers might be someone who has issues or is having a tough time, and who needs to talk with her; having a new person along might have prevented that completely. Or she herself might get very little time with this person and could rightly want her one-on-one time with this friend to be just that--one-on-one; maybe she hasn't seen this friend in ages and this is the first time they've managed to find time together. Or she might know, from experience, that this friend has characteristics that seem off-putting or odd to those who don't know her well already, and she didn't want to make you or her friend uncomfortable with an awkward meeting. She may have sensed that you wanted, as you put it, "girl time" when her time with this other friend is more about discussing the serious life stuff that old friends might need to discuss. She also might have had problems in the past when she tried to be social with her husbands' co-workers' wives -- that situation can be fine or can be fraught with problems....There may be a lot of reasons why she might not "mix friends" and many of them could be very valid and good ones.
By effectively asking her to invite you along on an already arranged outing....well, you put her iin a bind at that moment. I would admit that to myself and at another time very soon, ask her to go do something; she may be a terrific friend to you in the long run, but you will never know if you never try to go out with her again.
I guess the point is: I'd learn a lesson here about inviting myself along, and I'd give her another shot. You don't need to say anything to her or keep apologizing - you've done that and it's over. Get to know her one on one.
If you're still seeking friends, I'd try to find them in places where you have interests in common with other women. Volunteering, book groups at the library, a church or other place of worship if your family is religious, etc. are all ways to find people with interests that you share. Moms from daycare and wives of your husband's co-workers may or may not have anything in common with you.