Unless your taking the tags up the first base line was discussed with your partner during the pre-game, then I would say that it is the BU's call all the way.
What I can't figure out from your post is why the BU had to wait for the runner to clear before he could get in position to make the call. If he was in the proper position using proper mechanics, then he should have been in position to make the call already. Remember, if the ball stays in the infield, the umpire stays on the outside of the diamond, if the ball is hit to the outfield then the BU would come inside.
If for some reason he is still out of position to make what should have been his call, then he could always ask you for help. Barring him coming to you for help, or some kind of arrangement between you two at the beginning of the game, though, it is still his call.
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