Idk if it works on Bee, but as I used on my previous lineup Mabui/Tenten/Darui, I controlled who will be the target of Mabui/Azure standard heal when all of them have full HP, so I cn always cast her mystery despite prompt acupuntures/immobiles.
What I did was to "place" Tenten first into the lineup, before all other ninjas including the main. Now, you might wanna say "the main ninja cannot be removed from the lineup".
Yes, you cannot, unless it's Matsuri/Survival. Now, to make Tenten the target of standard heals, drag her up, and put her down back to her tile. Proceed to the next ninja
in the priority order, drag and drop on same tile. The last ones you will be dragging up and placing down would be the healers, or in your case, Bee.
I personally haven't tried this on Bee/Kurenai, and other ninjas that target allies. You can try.
As for the Mabui/Tenten/Mei or Darui team, that strategy works 100%. Certainly comes in handy in space time autos.

In short: The target of standard heals is the ninja that is "first" to be dragged up and placed down on its tile. Make sure you go all the way through the fourth ninja to make the priority order work. The fourth ninja to be dragged and dropped down is considered the "last" ninja, and thus, will not be the subject of standard healing unless its hp is the lowest (with suffered dmg).

Fun fact: The "ninja with the lowest life" description in most healing abilities is based on the targets % HP in proportion to its own total HP pool. Thus, if all your ninjas have full HP, the one with the lowest HP value don't necessarily get to be target of the healing standard. The system seems to calculate HP proportions relative to its full value, based on percentages.

That wasn't the case for me. I've had the same lineup, same positions for those ninjas since I gathered them up. I wasn't "moving" them anywhere. I merely lifted one ninja up, and placed them back to their own tile, following the order of making Tenten first, then Darui, Azure and Mabui.
However, it gets messed up when I change tabs, so I had to redo the order again when I switch back to that tab.