Mulch depth changes both how the bed performs and how much you need to buy.
How deep
Two to three inches is the usual range for garden beds. That is enough to suppress weeds and hold moisture without smothering the soil.
Coverage
One cubic yard of mulch covers 324 square feet at one inch deep. So at 3 inches, a cubic yard covers about 108 square feet. Bagged mulch is usually 2 cubic feet per bag, and about 13.5 bags equal a cubic yard.
Why not deeper
More than 3 inches can hold too much moisture against stems and roots, and thick mulch piled against trunks invites rot. Keep mulch pulled back a little from stems and trunks.