I haven’t read the complete thread, but I thought I’d put in my two cents.
Bridget is quite possibly the ONLY ggxx character that I can play and actually have a good chance of beating people with.
anyways…
My basic tactic is to corner the opponent.
A good way to start off a battle is to use S+2S (substitute 2S for 6S if playing against a relatively tall character). This will knock them back a bit.
Now you’re in a position of control.
Air dash over, and you should reach them by the time they are waking up. Do P+P+2S, and you should be on the ground by now. This leaves the opponents three ways:
a.) blocking
b.) in the air, being juggled.
c.) standing
if a: do: 2P+2P+2S until they’re juggled or standing, go to b or c respectivly.
if b: Jump up, and do P+P+2S (JI) S+2S. If you are below your opponent and you still have some time, you might want to do P+P+2S (JI) P+P+2S.
if c: Dash in and do (standing close) S (one hit)+S+2S+6S. This should leave them on the ground. You can repeat from the initial air dash into P+P+2S if you want to play rushdown, and the opponent is still pretty confused about what you’re doing.
It’s also good to mix this up a bit to keep the opponent guessing. Most of bridget’s rush down techniques can be subsituted with a few quick punches or one 2S in place of other attacks. Play around with him a bit to see what works best.
However, if you don’t get the upper hand in the beggining, you might be raped a little bit. Try to block as soon as you can and when you’re away for a while, (make sure the opponent isn’t doing an air attack), dash away and if you catch up with them, do P+P+2S.
If you’re still being harrased, start playing with your yoyos.
Do a standard yoyo-recall if the opponent is doing a potentially harmful attack. It should hit them, saving you.
Another good idea if the opponent is playing dashing games (ground or air) is to set a yoyo in the general area that they’re dashing in. Use the Roger Saw and if they dash into it, use bridget’s standard air combo (P+P+2S (JI) S+2S) (if in air), or a 2S+P+P+2S (JI) S+2S.
The only overdrive that you should be using is me and my killing machine. Please don’t try to do something spontaneous and use loop-the-loop, or the dreaded matinence attack. Me and my Killing Machine should pretty much slaughter a character if started close to him/her.
Trouble characters:
Testament:
There’s not much you can do when he starts using 2HS. Just bear with him and block, and attack when you get an opening. It also isn’t a wise idea to try to trap him in a starship, because if you don’t connect, he’ll probably smack you with 2HS again.
Sol:
Don’t try starship. Just don’t. Rushdown might not work as well as it would with other characters, so try to play mixup with your yoyos. Standard recall should trump his flying kicks. PLAY DEFENSIVELY IF HE STARTS TO DO THE DUST LOOP.
Potemkin:
Okay, he isn’t a problem character unless you get against someone who’s raping potembusters. If they aren’t, you should be fine.
I-No:
Don’t try to play air games when she has any tension that could initiate an overdrive. She’ll probably smack you with a final fortissimo. Other than that, just watch out for stroke the big tree, and you shouldn’t have TOO much trouble dodging her chemical love and air dashes (bridget’s pretty fast, surprisingly).
One more thing: If you’re stuck in a nasty combo, you might want to do:
Super jump + 6HS + 214K -> HS [when you pass the yoyo] + 2HS + 214HS. This should bide you some time to catch your breath (Mostly just stalling for time.)
Just my two cents 
Comment on any suggestions.