From the look of it, it is up to the GM. The feat doesn't specify.
Personally I read it more that it causes the two items to become one item, so it wouldn't be the sum of the two bulk. Bulk involves awkwardness of holding as much as it does weight.
I would probably go with that it has the higher bulk of the items - just because then the player doesn't have to re-calculate their bulk amounts every time they change their fused item mid-battle.
Another reasonable ruling would be that the item would have the bulk of the item that it is at the time.