Glennmac: The bridge you're looking at doesn't have to carry too much load so you're 4x12's should be fine. As an approximation, 2-2x12's on 12' posts will carry about 500 lb/ft or 6000 lb uniformly distributed over the 12'. Your load won't be uniformly distributed, but you'll have at least two beams. I'd space them so your vehicle drives over the beams - otherwise, the 2x6's will easily be the weak link.
I've been playing around with Sonotubes for some foundation work this summer. I put 12" dia. tubes on 2'x2'x12" footings. Mixed with a small portable mixer. For a 60" column it took about 45 min. I used 1/2" rebar in both the footing and column. With this little load, I'd just stick the bar in the column after you've got enough concrete in it to hold it in one place. I'd use a foundation bolt to attach to the beam. Use an 18" bolt so you're at least 6" into the concrete. If you don't put a footing under the 12" column, depending on the bearing strength of the soil, this could be the weak link (w/ poor soil, the column may only carry 1,000 to 2,000 lb ).
This is just based on beam/column design. I'm afraid I don't have any experience designing for washout.
p.s. from a beam bending standpoint, a 4x12 is close to the same as a 10.5" dia. pole