most tris have a relay category. sounds like you need to find yourself a buddy who runs.
fwiw - although ive done many tris on my FG, and as much as i espouse the need for 'needing' only one bike if you want to be somewhat competive in tris you've gotta have gears. Not that you cant be a strong force fixed on any given day, but if anything goes wrong in the swim, its nice to have a bail-out gear(s) so you can save your legs on the run. Its the run that makes the race.
If your wife isnt into FGs on her own, it could only make her tri experience worse.