The most important phrase here would be,
possibility of keeping the courtship going?
I would like to preface this by saying that there is no guarantee that Bob will be able to keep things alive. The development of a relationship should be mutual and should never fall within the confines of gender.
How might Bob tactfully decline the suggestion of going back to his place
Truth. Well-worded truth. Short & sweet, keep the point across. "Hi Alice, I would love to take things further with you, but I'm afraid that we are going way too fast. Don't get me wrong, I just want 'this' to be built on a pace that we are both comfortable with!" Normally these are sentences said by the girl, as you've mentioned above "arises out of expectation of traditional gender roles.", but I feel that it is pointless trying to beat the bush.
Tell Alice how Bob feels and hope that she respects his stance. If she doesn't respect his stance & is assertive of 'going back to his place' still, well it simply says a lot about her character, and Bob should rethink if he still wants to move forward with her any further. In this case, her character would be how she would neglect his boundaries.
This advice can be backed up by this article called "How to take it slow in a relationship so you don't ruin a great thing"
Since all of my relationships in the past have been riddled with co-dependence, I now make an effort to move cautiously and deliberately in my dating life — and I make that clear from the very beginning. That way, my partners don't take it personally when I actually want to get to know them instead of rushing into a relationship haphazardly. And to be honest, everyone responds well to someone who has boundaries and knows what is right for them.
- Make Justified Excuses & Reasoning
If you cancel plans without a follow-up, your partner might think you are potentially trying to ghost them instead of slow down the relationship because you actually see a future. Winter offers suggestions for slowing things down by saying things like, "I can't see you this weekend. I'm going to family event. How are you set for the following weekend?" or, "Tuesday night's not good for me. I'll be out of town for a client meeting. Could we touch base when I come back and have a better idea of my schedule?"
This way, your relationship will have more appropriate pacing instead of falling into the dangerous "I like you, let's hang out with each other every day" zone, which is something I am definitely guilty of falling into. Secret: Those relationships tend not to last.