IMO it's built that way a bit intentionally to make you spend gems.
Simply fuse with any unit of the same BB type: attack, heal or support.
BB level resets when evolving so it's near pointless to do it before their final form. In the three I've done so far it was around 1/30 for a single level up... so 300 fuses to get to rank 10. It is significantly less expensive to start at level 1 but it also holds you up for quite some time in doing anything else until that's out of the way.
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