My experience:
Got CT for Christmas last year (had a button mash fest at a friend's house prior, had loads of fun). Played for about 3-6 months just for fun: no real combos, using the special shortcuts, etc (started pretty much from scratch in FGs). After I started beating the computer consistently (no XBL, no interested friends) using these techniques, I slowly taught myself how to do these inputs for specials, and integrate them into my gameplay. Played all of the characters a lot, so I know what 99% of the moves look like in BB, though not necessarily what's in combos and stuff. Found DL, dropped Nu cuz she was high tier, and played Litchi with her excellent pokes ('cuz my litchi combos were gatlings or three dragons).
At the beginning of CS arcade period, Rachel seemed low tier, so I started practicing combos on training mode. Never got far, found that I'm not one of the few people who can play low tier at a high level when I bought CS. CS challenge mode is probably my first big step in self improvement; for some reason the movelist on the screen kept me at it longer than jumping in training mode.
But even after I picked a main and played a TON of matches (and even trying to teach other people the game at college), I'm still one of the freeist players in the Michigan thread (since any local scene is too focused on school to be playing a lot w/ me). Considering where I started, I came a long way; it takes time, though admittedly my CT time was for fun/prepping for CS.
I don't know your fighting game background, or at how fast a pace you are capable of learning, but if you want to get really good at this, it's gonna take up a lot of your free time. It's pretty rare to be playing other types of games and find someone who knows Blazblue. There's a reason why.
If you still want to spend the time, follow some of the generic advice in here: practice combos, read up on forums, watch videos. I don't recommend starting with Ragna unless you want to main him (and the longer you wait to pick your main, the longer it will take to learn the game).
...my story and advice, 2AM quality.