It was hard to judge from the initial post whether or not he speaks to her when goes through the till so I'm assuming he does.
First of all, there are a number of questions that can be asked that can give you the answer without asking directly. Asking what she did the past week or planning next weekend are always good ones especially if he's not in a rush as not only will he find out (3 week with no mention of a bf and you're 80% safe), his remembering what she said the following week and referencing it in the conversation will make him seem more thoughtful and increase his chances. We're also coming up to Christmas so asking about what sort of thing shes planning is a good one. I don't have a great deal of practice at doing this and even I can get someones relationship status within 20 minutes of conversation.
Secondly, there's always the non-date option of "I enjoy chatting when come through so fancy meeting for cup of coffee one evening/weekend?" This has the bonus of being quickly turned into either a date or friends meetup without him being embaressed. If she says yes then they meet up and he has more time to check the waters and make a move if its safe. If she isn't single and she mentions it, you mate can go "Just as friends" and nothing is lost.
Finally, he could just grow a pair and ask her out
