I did a look up of bike rental shop in FW and this is what I came up with.
I have never dealt with this outfit so I have no recomendation on them one way or the other, or even if they are still in business.
Phil's South Side Bicycle Shop
2310 SW 336th St.
Federal Way, WA 98023
(253) 661-3903
Rent hybrid and mountain bikes by the day.