The swarm hotline gets a few calls every year about bumblebees in
bird-houses.
Usually it's about an established bumblebee colony that needs to be
relocated.
I recall our being asked to relocate a colony in a cabinet or shelf on
someone's porch.
There are 30 or 40 species of bumblebee in the US. Territories overlap
in our region, and
others have different ranges.
The "farmed" bumblebees, when taken to other regions can disrupt the
success of the indigenous populations.
(why would someone manage bumblebees? They are a terrific pollinator of
(hothouse) tomatoes for instance.
The queen may have already started building cells. Can you set up a box
at that location just for the bumblebees,
and carefully move that nesting material into it? - and move the owl
box a couple of feet away?
One presumes the bumblebee queen navigates to a home location like honey
bees do... by landmarks to within a few inches of the entrance.
that's my 2¢
The hotline had a caller a month or two ago that had a bumblebee colony
in a particular birdhouse they
expected to be reoccupied by a pair of birds that visits the porch year
after year.
I suggested providing a second birdhouse the birds could use, so the
bumbles could finish their brood cycle.
Once the bumbles finish, that birdhouse can be cleaned out.