What is the best strategy for going past bridge?

This may be a bug. Stellalune at Tomb Raiders Net describes it:

"Near the end of 'Part 1: The Unnamed Days', there is a fork in the path where the player can choose to go left or right. If you go to the left and Lara dies before reaching the next checkpoint, this can trigger a bug at the beginning of 'Part 3: The Midgard Serpent', in which a certain set of ramps, which allow you to cross a deep pit, are missing, preventing you from continuing in the level."

Either download a save from Tomb Raiders Net, which isn't possible for the 360 as far as I know. Or restart from a save before the fork in the path in "Part 1: The Unnamed Days."

When you jump the 1st pit you may notice some poles sticking out. When you get to the 2nd pit, there are more poles. Jump up the pair of poles and jump onto a ledge which will raise the ramp. Oh yeah, spiders will come to attack you once you drop back down.