There are several threads on paying for hotels. Search box there 👆 .
If you are only using the hotel for the punt, consider having the girl book it for you. And if only for a short time consider a day booking. I have a punting PAYG card as well as a punting phone - comes in handy a lot. Currently using Ffrees but Kalixa was fine also.
But anyway when you check out just say you will pay in cash.
One more bit of advice is to have a dead simple story ready incase something unexpected happens. The simpler the better. But make it up in advance so when she says, 'My friend saw you in the lobby blah de blah', without missing a beat you say in a bored way your story.