If you want to learn blues guitar the first thing a teacher is going to ask you is what experience do you have on the guitar so far? Maybe you've never picked up a guitar, then they might ask you if you have any musical training: piano? voice? other?
Then they might want you to show them some of the more interesting things you can play, just some samples so they can evaluate your present skill level.
The next thing they should ask you is what Blues Guitarists are you interested in?
This could be anyone from Robert Johnson to Albert Collins.
If you don't know? Then you need to do some homework. Here's a list of blues musicians you should listen to and get a sense of history (1920's to present) not just guitar either.
Pine Top Smith (piano, boogie),
John Lee Hooker,
Stevie Ray Vaughan,
and Buddy Guy
And this is just the tip of the ice berg, here's some more:
In any musical instrument instruction you should receive some of the following: theory, history, technical exercises (such as scales, arpeggios, chords, positions), expressive elements (vibrato, tremelo, bending notes, slurs, slides, hammer ons, etc), learn pieces, play duets, play solos, play in an ensemble.
Update and edit based on comments:
"Love me some BB King and John Lee Hooker." and
"...still read sheet music for choral singing having done a few years of cornet in middle school..."
So you have some great tools to work with and a focus on who you like.
Some people will argue that reading music will not help, but since there are a number of people who have transcribed earlier blues music your sight reading skills will be of use.
For the most part, like folk music, much of blues is by ear, so ear training is recommended as well. Don't worry, any good music school would teach both ear training and reading skills. Most professional blues players that I know personally play by ear, and can learn a 'riff' or 'lick' almost instantly. A combination of good ear training, knowing the guitar finger board up and down, and some natural talent is all good.
Your experience with the cornet will assist in understanding melody and expression.