3rd rail splines exist. Just add it in surveyor about 2 ft from either running rail but this methed won't work for a moveable bridge as the 3rd rail spline would not move when the bridge opened or closed. Trains actually cross moveable bridges on invisible track. The ties and rails you see are parts made to look like ties and rails and are part of the mesh. The 3rd rail parts would have to be part of the mesh as well.
I'm not certain there are any track splines that include the 3rd rail because of the way track splines are made. See page 74 of the Content Creators Guide. The values are symetrical. There doesn't seem to be any provision for a 3rd rail (but hopefully I'm wrong, lol).
Lay the bridge as a separate spline about 0.2m under your track spline, and move carefully into position without connecting to your running rail(s). This is also worth considering for any track if the track on the bridge you want to use is significantly different in appearance. You won't get the bridge "rumble" but it will allow you to use pretty much any structure you like.
A bit trickier where the bridge is curved or on a gradient but with enough spline points plus trial and error it should be possible to get the bridge positioned so its own track is hidden.
There's also a couple of trackless viaducts and bridges in the default content from '006 onwards (not sure if in TS2010). These can be placed in a similar manner.
The answer to that is to keep doing it until you learn to do it smoothly. Any skill takes practice to master.
In the meantime, check Jaleel's content. He did some 3rd rail assets. a search for 3rd rail or third rail (or other variation on the description) should turn up a few bridges.