Mominul Haque and Shadman Islam steadied bangladesh after losing Soumya Sarkar for 19.
Devendra Bishoo's double strike in the second session brought Windies back into the contest.
Shadman Islam and Mohammad Mithun added 64 runs before Bishoo struck to get the pair.
Mushfiqur reached the landmark of 4000 Test runs before he was cleaned up by Shermon Lewis. He was the last man to fall before Bangladesh ended the day on 259/5.