When a girl says she needs time after a bad break-up?

Is it true? Is she really just not ready for a relationship. Does she really just need to be single and not have any commitment for a while?

Even if she says she really likes you and would like to be with you - but is afraid to let someone in to her heart so soon after, that she can't trust anyone like that just yet? If she doesn't want to stop seeing and talking to you, and actually initiates conversations with you when you said you shouldn't talk. And if she hunts you down while out and asks why you're avoiding her, and if you deleted her number, and if you're seeing other people, then gets sad (even though she is too). Should I respect her decision, give her time, and some space, and wait for her (assume she's worth it - cause she is)? Should I just take her out some times, show her I am genuinely interested, and take things slow?

It was a nasty break-up with her ex, and we did start seeing each other soon after it. I can see her not being able to commit right now.
When a girl says she needs time after a bad break-up?
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