I had a very similar situation with my bun Chloe, I would have to chase her into a corner to catch her, or cover her the same way you mentioned. I really don’t recommend this, as it’s just making your rabbit associate your presence with being stressed or trapped which isn’t a great for the bunny/owner relationship.
I started to use raisins, as soon as I opened the container she was out from hiding and begging for her delicious treat. I put 2 raisins in the food dish in her hutch so she’d have to go in for it and then close the door behind her.
My opinion is that a routine is key. So I did this every night around 8 or 9 PM, and after a few weeks she was going into her hutch around that time when I hadn’t even put the raisins in her dish yet (AMAZING!) and I continue to put some sort of reward in there for her now, not always raisins.
If you’ve just started bringing your bun into the basement, it’s just a matter of introducing a new routine in which your rabbit is removed from the room in a positive way rather than a chase. Lots of good suggestions are above, just pick the treat that you know your rabbit can’t resist most and only make it available when you need to put them to bed
Good luck!