Hi Shifty,
You should ask her out immediately into the conversation.
The danger of waiting it out until the middle or end of the conversation is that, you may rely on the conversation to go a certain way so that it feels more natural to ask her out by the middle or end of it.
This could easily put you in a position where you don’t quite know when to ask her out because the conversation hasn’t reached the level where you feel the most confident in doing it.
This could cause you to delay asking her out, only to discover that by the end of the conversation, you still don’t feel comfortable doing it.
It is best to ask her out immediately so as not to rely on how well a conversation goes in order to do it.
Just get it out of the way.
Then, you can proceed to have a conversation with her.