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I'm also stuck at this spot, and I've spent half an hour shooting everything to no avail.

Okay so.. This room has been reworked in future versions as it was causing problems for people and the bridge felt a bit pointless as well.

So here's what you have to do:

Start running from the previous room to the left and you should be able to run over the bridge.

Thanks for the reply!  Your tip helped me to get through that part of the map and I was able to complete the demo, the rest I really enjoyed.

I think the reason I got stuck is that I didn't notice that much of a difference in speed between beginning my run in the room and starting in the previous room, because I took one look at that room and figured that I had to find a way to move faster, much like how a similar room taught me to run in Super Metroid.  Thanks for your help!

Yeah, that's because there actually was barely any speed difference, another reason this has been removed.

Glad you like the rest of the game though. :)