A coworker (A) had her birthday on Thursday, to surprise her, another colleague/friend (B)and I decide to buy a gift for her. The gift ended up costing around $45. At the checkout, I paid with my credit card, and coworker B is supposed to pay me back around $22 in cash.

It’s Monday afternoon, I’ve seen coworker B more than a few times today. But she didn’t mention anything regarding giving the money back. How should I bring this up to her? Should I go up to her directly and ask for the money back? Or will she think bad about me?

It’s not a large amount, and I can chalk it up, but she was the one who really wanted to buy a gift together. I would have otherwise just bought a small gift to A, my original budget was $10, and I ended up paying over $40 . Did she simply forgot or does she simply not want to pay?

These are very simple things that most people make too complicated. Think bad of you....HUH? That makes no sense.
The fact is SHE should have paid you the next work day or mentioned that she would pay you on Tues or Wed.
Even if she forgot that is still not very good manners.
Keep it simple, "Hi Sue, I just wanted to remind you about the $22 for the gift, can you bring that in tmrw morning? OK, thanks." If she says anything else beside OK, your response is simple....I am sorry, but if you did not have the money you should not have bought the gift. I have a policy of not loaning money to co-workers, so we should get this cleared up tmrw.

Not that you are sorry to ask, or that you have a bill to pay, or if she needs another week you can wait, or any other non related issues.
People respect those are direct.
a>

Yes, ask her politely "Hey can I have my money tomorrow if possible for the gift we bought for such and such person".

Don't over think it.

Send her an email.
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Subject: Birthday Gift.

Forgot to remind you on Friday -- don't forget you owe me $22 for A's gift last Thursday.

Thanks,
Your Name.

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