Hi Natalie
I've got no idea where '8 bars of cycle of fourths starting on C' is meant to get you, but here's my take on Confirmation and recital improv strategies that I've used:
Ok, so you know the form, therefore you know its AABA 32 bar blues, commonly known as 'Bird Blues'. That means 3x8 bars (3/4) of the tune uses the same 8 bars of changes. I assume you're an alto player, so you're playing it in concert F.
Different levels of improv for recital:
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1. You learn an entire solo you dig, note for note.
PROS: sounds great, really works your memory, you pick up all these really cool sounding licks that you have no idea why they work, they just do!
CONS: if you make a mistake and lose your place, you're probably screwed for the next 7 bars; takes a day of solid concentration and mucho repetition
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2. You learn fragments that can be used in critical areas.
Eg the 3 to b9 lick Bird was famous for. This is written about in several book/CD sets with analysis of why it works.
PROS: moments of brilliance, easier to handle cos it's bite-size and it'll give your solo some street cred; quick to learn and apply and you know they'll work
CONS: snobs will label you 'cliched'
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3. You dig deep and play the blues tune over and over, then drill the major and minor ii-V7s relentlessly til you find the two 'merging'.
Ok, so the A sections are basically I-vii-iii7-vi-ii7 [d] then a ii-V7 to the IV [g] followed by iii-vi7-ii7 and a ii-V7 back to I again.
The B section is a straight ii-V7-I [G] then ii-V7-I [Bb] with a ii-V7 to get you back to I [D]. Rinse and repeat the A section again.
Notice there are alot of ii-V7s in there? If you're looking to cook on this, you'll need to have some ii-V7 ability, both major and minor. Now get tactical here - practising ii-V7s in all 12 keys may happen eventually but why not work the 6 specific ones that you need for this?
Er, I think: (alto key of D) C#m7b5 to F#7; Bm7 to E7; Am7 to D7; F#m7 to B7; Em7 to A7; Cm7 to F7
PROS: With your strong hold on the tune, you'll be confident enough (and technically able) to venture into some 'change running' (initially) and then maybe some more advanced stuff (like tritone subs etc)
CONS: if you don't get any of number 3 past the bit "learn the tune" then it all may sound like maths...
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4. Let inspiration take you, based on your current technique and hearing
PROS: you could stumble on something really hip and impress the heck outta everyone in the room
CONS: you don't, and in hindsight become a blithering mess of D pentatonic, missed chord notes and zero voice leading, little chromatic resolution and in fact the tune goes out the window too
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I use number 4. all too frequently but the work I put in now is a combination of 1, 2 and 3. I used number 1. at jazz school and I recorded more misses than hits with it BUT it's a brilliant way to inject alot of new material into your vocab all at once.
Be kind to yourself - if you haven't got a clue about improv theory etc BUT you can carry a tune for a mile n a day, just play the melody and embellish where n when you can. This is still improvising and some of the ol guys I've played next to use this approach "cos that new fangled stuff sounds ****e"...
Long winded? Yep, but there yer go. Some of my experiences in 4. point approach to improv when time's against you and your guns are jammed.
Have fun!
Simon