Do I pursue her or let her come to me? Confusing situation.

I asked this girl out last month after flirting for a few months before. We had talked about how we should do something together, but when I asked her out she said she was kinda talking to someone else now and she would let know if things changed. I've spent the last couple weeks trying to get over her because I was pretty down about it, until last week.

Last week I was talking with her at work (inb4 coworkers are off limits;it's a small part time job for both of us while we are in school). She ended up giving me her number saying we should walk our dogs together sometime. This is where it gets difficult for me:

I texted her this weekend when I was taking my dog out inviting her to come along, but she was busy with family stuff and told me to let her know another time. If she is still involved with someone, I feel very uncomfortable texting/ contacting her regularly or inviting her to "more-than-friends" activities (walking is fine). But she is also not the type to come out and say "I'm not seeing anybody anymore, let's go out sometime." I don't want to overstep my bounds if she's involved and I don't want to miss my 2nd opportunity at her if she is available now. Should I risk being more forward or sit back for a bit longer and get a feel for what her situation is and let her tell me when she is available?
Do I pursue her or let her come to me? Confusing situation.
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