This is what I did as a kid. It has a basic logic to it, and you may find it a good plan to follow.
Find a 12 bar blues that you really like the words of, and learn them. Then when you are away from your instrument about your daily work or whatever you can keep singing it to yourself in your head and/or hearing the original singer.
The 'changes' will start to sink in and you won't have to count - you will feel them.
Listen also to some blues where the rhythm section is prominent, and listen for the changes. Boogie woogie piano is good stuff for this, too.
Your first improvisations may well be quite basic and sound a bit like some early jazz. That's great - it's the basis of the thread of blues which runs through all later jazz. Once you can improvise happily and 'to order' at this level, listen to how more recent jazz musicians played. Follow the time line in your listening, getting the feel of each era. Practice doing the same until you can do that too, before you move on.
You will notice that a key element of later jazz is a much more fluid use of rhythm. You may well find that moving from the older style of phrasing and how it relates to the basic pulse to later styles - particularly bebop - takes quite a lot of practicing to get right.
If you keep trying to imitate (I don't mean simply slavishly 'copy' or use transcriptions) the sort of stuff you hear - in a sort of musical time journey - things will fall into place.
It takes a lot of practice, but make it fun with a minimum of stuff on paper (writing out a schema of the changes is a good idea - visual memory is powerful stuff) and it will all come together. Phrases will occasionally pop out of no-where and surprise you 'cos they sound just like real jazzers play... the more you do it, the more it will happen.
By the way, you don't have to chuck away jazz from earlier eras as you progress. Listen to Mingus. His Blues and Roots CD is a good example and very aptly named. You can hear 'everything' in Sonny Rollins' playing, too, and many other players. Charlie Parker played the blues a lot - he just did it in a way that you need a quick ear to hear it all...