Decided to throw caution to the wind, call the number on the back of my card and see of BofA would pat me on the head for good behavior in the last 8-9 months since I opened my accounts with them. Wasn't instantly approved, but CSR said one of 3 things happens, with phoned-in CLI requests: the letter-in-5-7-days message (usually if not always denial), instant approval, or transfer-to-credit-analyst response. I got the last one and managed to get a $500 CLI on the smaller of my two CL's to make that CL $2K (the other's at $7K, which is fine with me - it's my highest CL so far).
The larger CL is BT'd and so in the sock drawer, but I did want/hope to get at least something on the other one, which I try to use, for my good behavior, so I was glad the credit analyst gave me what he did.
Questioned me about my short credit history (a bit under 3 years) and income, asked if I'd had a BK (no).
Forgot to ask which CR he was looking at, but my scores as of a couple weeks ago were TU 718, EQ & EX both at 693, overall util ~23%.
I didn't do the online request because the last time I tried that, my 'CLI' actually turned out to be just a transfer of part of my BT'd card's limit to this one - ack! I called as soon as I realized what had happened and had them put things back.
Just FYI, for anyone hoping for a CLI from BofA - I figure I'm a so-so credit profile, right now, and they were willing to give me one. A nice way to start the New Year! 
Congrats, Scamp!
CLIs are great, and that conversation you had sounds very similar to the one I had last week with the very nice underwriting person who doubled the CL on my brand new BofA card (this after I'd already got a small CLI at activation) after asking me all those questions you mentioned. Sounds like they're very far from just dishing out CLIs willy-nilly, but it's SO nice when they look everything over and come back with a nice increase.
Congrats, Scamp!
I only have a few more months till my partially-secured graduates. (At least I hope it does--no guarantee, I know.)
But hearing about BoA's cli's to folks makes me happy I followed advice to get one.
EQ 817, EX 815, TU 813 (Updated 1/5/18: TU 843
Thanks everyone for the congrats!
And to nicemann - ain't those CC Backdoor Numbers great? 
I think I'm about at my ceiling with BofA for my current income and debt load, so I don't blame them a bit for being conservative with me right now. Some aging of my accounts and reduction of balances may earn me better increases over time.
congrats!
curiosity got the best of me and i hit for luv a few weeks ago on my card w/ a bt balance to try and get a little additional padding as i pay down briskly. i almost wimped out at the last second. well, with all that's going down... now i'm sure glad i took a chance- Bingo 300 instant cli 3000 to 3300. i heart boa