Did you do this yet? Check out
https://www.engineeringtoolbox.com/f...an-d_1479.html, which gives span tables for residential floors.
It shows that 2x12 select structural (fir around our parts) will span 25 feet if you put it on 12" centers. So if the bridge is ~36" wide, you have your two outside and one center joist, and that should EASILY span 12'.
Of course, I imagine you are using treated, so that is a little weaker.
https://www.decks.com/how-to/41/deck...ng-and-spacing
Anyways, I would have zero concerns about making a 24" wide and 12' long bridge with 2 2x10s on either side that were bolted together. That should last a lot longer than you need it to. If you bolt/glue two pieces together, consider putting a joist protector on the top to keep water out from between the two members. Like
https://www.amazon.com/Grace-Vycor-P...dDbGljaz10cnVl.
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