If you are planning to T2 BM then you should MRUT BM and get the 256 bios to aid in the upgrading of his gears. I didn't do so and am still farming his bios from SHIELD lab. If not, you might as well just finish the last stage and get him at 6 stars.
If you do not MRUT BM, then what you are waiting for exactly? Are you waiting for normal RUTs to rank him up?