The size and spacing of the joists under floor is what determines how much weight it can support. If by "bowing" you mean that floor is sagging, rather than a slope, it would be wise to check joists to see what you got.
Apart from the labor involved in removing existing flooring, it is easier to level a floor from joist level.
It is easier to put in furring strips across the slope than trying to cut long tapering ones. Glue and screw them thru existing floor into joists below.
Also check for any creaking from floor you have now. Screw loose flooring to joists.
If slope runs along joists; one end higher than other, or ends higher or lower than middle;
If the "right side" is 3/4" inch low I would put a 1 1/2" X 3/4" strip the full length or width of that side. You could use plywood or rip it off a 2x. Come 16" closer, to high side and measure height for next strip, rip it from 2X, and glue & screw it. Continue on untill you reach high side.
If slope is across joists put strips on top of joists, you may need some in between joists .
Glu and screw underlayment on strips to joists below. You mite want a light weight filler between strips as a sound deadener. This does not have to be as watery or heavy as self leveling cement as you can screed it level with a board dragged across strips. there are "concrete" mixes with light weight aggregates.
Measure twice, cut once.
Look at the nail, not the hammer. Watch the fence, not the blade.
If you hook your thumb over your belt you won't hit it with the hammer or leave it layin on the saw table.