building a lawnmower bridge

Your best bet to construct a curved structural member (on a reasonable budget) is to build a glue lam. Keep in mind that the bridge in the photo is probably about 16' long. On a 8' span 2' of rise (probably less) should be plenty to replicate the look. You can buy 4 sheets of 3/4" pressure treated and rip them in half. Now make 2 stacks (8pcs) of 8x2 sheets glued together. Put your glue on with a roller and screw it together. Then trace out your curves and cut. When you're done poly the hell out of it. This will give you 2 curved structural members that are 6" wide and WAY stronger than traditional lumber.

Actually 2' of rise is way too much for an 8' span (your mower will bottom out). So rip it at 16" wide and then you'll get 3 arches which will help support your decking and prevent the whole structure from twisting.