It might be worth asking if there are headphones that will NOT work with the B2.
I took a punt on some EvoDX BT5 noise cancelling headphones (~£30) and these worked fine. I bought these from 7DayShop but they are no longer listed there. These do appear on Amazon but are shown as "Currently Unavailable" so you may have to do a bit of searching to find these.
Like you, I have a BT speaker and that worked fine and I expect that there will be plenty of BT devices that will work.
Good luck!
Peter