If you can find them, 20 foot pressure-treated 2x12's spaced 12"
apart should span your stream nicely. I would add solid blocking
every 4 feet or so to add some lateral stability and prevent the
joists from twisting.

Ya' think!!!!???
Presuming 3-ft wide deck, that'd be 4 2x12 -- compared to the calc's
above that would support roughly 4500 lb mid-span w/ 1/2" deflection.
I don't think there's the intent to be able to drive a car over it...

Hey, you can never be too careful...

The original poster mentioned the current bridge was bouncy. I don't think
the usage was mentioned. If it's just for one or two people to walk across,
yeah, you could downsize the joists and/or spacing. If you need to drive a
couple of quads across the bridge, or push a fully loaded wheelbarrow,
better to play it safe.

You never know if the bride's entire wedding party is going to pose for
pictures on your new bridge. That or a bunch of drunk college kids.

Those were, as noted in the other response, based on an actual span of
16-ft, not 20 as the pictures made it pretty clear the extra length
was simply supporting the ends of the logs on the banks and all needed
for a bridge would be some piers at the edges at about 16-ft or
perhaps even closer if went down the bank just a little and left a
foot or so overhang each end...

I didn't take the time to calculate loads or look up spans in my charts. I
just used an online joist calculator to do a quick estimate. I went with 20
foot joists so there could be a foot of bearing on each end, and an 18 foot
free span. That would give a little extra on each end so the footings
aren't so close the edge of the stream.

Anthony Watson
www.mountainsoftware.com
www.watsondiy.com