I've had the exact same issue.

There could be a burr in the saddle. You can take it in to a shop and they can deal with it. If not you can replace that particular part of the bridge. I ended up having to do with with a guitar I used to have and the problem was gone.
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Like said look for a sharp point where the string is unwinding.

Check out string saver saddles or similar.

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Have I placed the saddle wrong? Maybe the screws are supposed to be on the other side?

Found this on wikipedia, and now that I looked closer, it's exactly what happened:
Over time, particularly on the thinner unwound E, B and G strings - the groove cut into the saddle, in which the string rests, takes on a sharper 'V' shape - due to the action of the string sliding slightly in the groove: particularly during string bending. As this 'V' shape sharpens, it takes on a slight scissor characteristic and gradually any new string is abraded as string tension pulls it deeper into the groove: this leads to increased breakage, particularly during bending - exactly at the saddle. The simplest solution is a slight filing out of the groove, to recreate more of a 'U' shape, while saddle replacement - particularly with very high quality metal alloy replacements, is another option.
Like the people above me said, it's likely that there's a sharp bit on the bridge that's tearing your string. If you find one, you can try file it down a bit, and then rub the tip of a pencil on it a bit - the graphite will lubricate it slightly and make it slightly less likely to tear.

That stuff should fix your problem, it comes in different gauges but my internet is ridiculously slow tonight and I can't get the page to load... I can't even get a Google search to come through
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