Your link contains a malformed vid id, but I'm assuming you're talking about http://www.youtube.com/watch?v=6aMirwQ2Rbk vs Bridget?
First read http://dustloop.com/forums/showthread.php?t=5473 Macarthur writes very good matchup info (I THINK HE SHOULD WRITE MORE, MAYBE FOR EVERY CHARACTER VS SLAYER WINKWINKNUDGENUDGESAYNOMORE).
I don't have too much experience with the bridget matchup but one of the obvious things I see is you're letting him use some really shitty corner pressure on you for free. When he stops mid pressure to yoyo set, DO SOMETHING! You shouldn't be afraid of bridget, YOU'RE SLAYER. Get used to IBing his obvious strings and either poke back or just jump/bdc jump/1f jump/etc out of the corner. You also missed a lot of free damage. You hit with a lot of 2h's and you had lots of tension to burn, you only need 2-3 combos to end the match. I also saw 2p-2p-2p and then you tried to 2d a couple times, hit confirm them into 2p-2k-2d for the knock down or 2p-2k-2h-BBU/DOT if you have some extra tension.
Random BBUs/Supers = big nono
use your tension, slayer gets tension very easily
try not to get caught between bridget and his yoyo
dont get hit by gold bursts , if bridget whiffs a gold burst, GET ON DAT ASS. that means you get to use your silly oki on him for FREE. If bridget guesses wrong twice, you win. Don't be afraid of his "dp", its terrible.
use your bursts smarter, dont burst because he poked you from mid screen
work on utilizing slayers ridiculous abare aka turn random hits into game winning combos
slayer is more invincible than everyone else , bdc 1f jump or bdc mappa/dot/whatever obvious pokes
I personally just like to land one big combo or so and play super safe for the rest of the round and either win by time out or by bridget trying to get in and dying by pokes.