Baker lost his opening serve, but broke back to take the first set to a tie-break. Bloomfield raced to a 4-0 lead before winning 7-4 at Scotstoun.
One break of serve to the English No.6 seed in the second set was enough to take the match in straight sets and set up a semi-final with the German No.3 seed Bastian Knitell, a winner over Alexander Ward 7-5, 6-2.
Baker now travels to a Futures event in Cardiff in a quest for points to gain entry to qualifying for the Australian Open.
The other men's semi will be an all-British affair with qualifier Ashley Hewitt playing No.8 seed Neil Pauffley.
Hewitt enjoyed a 6-2, 6-4 win over top seed Joshua Goodall with Pauffley beating Dan Evans 6-0, 6-3.