If she is asking you to meet her, make sure that you are clear on her intentions.
In other words, you should find out if she is looking to meet you as a friend or if she is interested in you as romantic potential.
If she makes it clear that she is interested in you romantically and she wants to meet you on that level, you should meet her.
Try going out with her a good number of times before trying to make her your girlfriend.
She may have avoided the topic of becoming your girlfriend when you asked her to be because she wanted to spend some time going out with you first.
She may have wanted to get to know you through conversation and shared activities before either agreeing to become your girlfriend or not.
This would be a better approach to use as opposed to trying to make her your girlfriend right away.
This slow and steady approach with her may help you ultimately convince her to become your girlfriend in the foreseeable future.