In short, I would recommend increased exposure, learning to play specific songs by ear, and having a reference book.
There are always a few different ways to go about learning a new style. One of the more important things is to listen to that style as much as possible. This will ingrain the feel of the style. You can learn a lot of theory from books but that will only get you so far. I have a whole lot of Classical theory (went to school for it) but my writing sounds nothing like it because I have not focused on it and don't listen overly frequently. With that theory I could certainly write closer to that idiom but it takes a lot more thought to be able to. Real point being that the more you listen to it, the more it becomes a part of your style.
The best way to further that sort of learning is to transcribe as much as you can. By learning to play what the greats did, it really sinks into your hands. It's also a much more involved way of listening. It takes you from hearing and feeling, to knowing what notes and rhythms are typically used within the idiom that actually create that feel.
That being said, Jazz theory, while rooted in the same concepts as Classical, is fairly unique. There are a lot of the rules of Classical music that are (somewhat by necessity) completely abandoned, voice leading for example. So having a reference to the theory can be very helpful. There are many books on Jazz theory but the one I am most familiar with and is used in the academic community is Mark Levine's 'Jazz Theory Book'. I learned a great deal from it, personally. A book can be very helpful to provide some insight to things like Extensions and Alterations, which you don't see a whole lot of outside Jazz, though they certainly do exist.
To best learn any style of music, you should try to fully immerse yourself. Allow it to take over your musical world for a while. You can still take some breaks to listen to or play other music but try to keep that to a minimum for a while. I'd say that after a few weeks to a month of full immersion that it would be a good idea to kind of step away from it for a few days, then fully immerse again. That will allow your brain a break and to get back in touch with other styles that you have enjoyed. Then when you return to the Jazz studies you may find increased desire and a new outlook/perspective on the music itself and how to best replicate it. Basically no matter what you are doing, it is always best to give yourself some breaks because it will actually improve your learning ability.
Lastly, even though it sounds like it may not be an option for you, I would very much recommend getting a teacher. A good teacher can recognize what you are doing poorly and what steps to take next for the best approach to learning.