I thought about this at lunch yesterday and thought something wasn't right. Plus there was another guy saying something about The Fallen and Sentinel. So here we go: Back in ROTF, Jetfire sent the himself and the humans to Eygpt (Or was it Vegas?) to look for the Matrix. Thing is that he used his hands to send them thier. Then fast-forward 2-3 years later into DOTM. When Prime revives Sentinel on low energon, he starts blabbing all about the pillars and how they work and blah blah blah. Then when he brings all the Decepticons from the moon, he's using the pillars. So how is it that we go from traveling from someone's hands to using pillars?
Sentinel is old, like our 60. Jetfire is ancient, like our 100. The Seekers had the ability/technology to teleport at will, but that technology was lost during the Fallen's made purging of the Primes. Sentinel managed to reinvent it to an extent, but no hand teleporting yet. Unfortunately, Jetfire scrapped himself otherwise he might've been able to share the teleporting technology with the Autobots, making them even more OP.
Okay in ROTF the space bridge was a psionic ability, similar to Nightcrawler's ability to teleport. Only a few Transformers, like the Primes or the Seekers had this ability (as seen by the Fallen and Jetfire). In DOTM the space bridge was an actual transportation device, similar to Heimdall's Bifrost or DR WHO's Rassilion thingy (which is why I found the ROTF one better). It can transport matter through time and space. http://www.tfw2005.com/boards/transformers-movie-discussion/549258-space-bridge-better.html
Built-in Space Bridge components are like die-cast construction - they're lost arts. I'd have to agree with what QLRformer said, it was a technology that was limited to a select few Cybertronians, and as far as we know, only to the The Fallen and Decepticon Seekers. And with the ability to transform being widely spread, it was probably a dying ability. Plus, Jetfire wasn't using his hands to teleport, he was "wrapping" himself around the human characters so they'd get pulled into the Space Bridge as well.
It's the difference between birds having the natural ability to fly and us needing a machine to do so. If we were birds that didn't have the natural ability to fly.
Everyone else here has basically answered the question. Simply put, Jetfire, as a seeker has that ability "built-in". Sentinel had to harness that power in devices. An extremely accurate analogy right there, folks. This is probably the simplest way to sum it up. Gingerchris, I salute you!
I don't think Jetfire spacebridged as he did telaport. Jetfire had Skywarps powers. I'm not really sure that counts as spacebridge tech or not.
Simmons: "...you're just lucky that I didn't get hurt! 'Cause if I would've gotten hurt, you would've heard from my mother!" Jetfire: "Oh, shut it! I told you I was opening a space-bridge! It’s the fastest way to travel to Egypt!" Sam: Tell us? Tell us? You didn't tell us! You didn't tell us anything! Why are we in Egypt!?!?!" Jetfire: "Don’t you get snippy with me, fleshling! You were dually informed!" Plus, either the writers or Bay himself said during production that due to Shia's hand injury, they were going to be writing it into the story. "There's this thing called a spacebridge where they teleport. And Sam hurts his hand in a spacebridge accident." (or something akin to that)