Impressive that you already have THE book recommendation already given in this thread. Dan Haerle's is nice in that he doesn't give short shrift to the importance of the harmonic minor and its modes (which, as you transcribe, you'll see is pretty key to understanding a lot of Bud Powell's music and other bebop) unlike the fashion to stick to melodic minor (ascending), sometimes just called "jazz minor."
I would just warn that there is a lot of misinformation in jazz pedagogy out there -- everyone seems to have some complicated-seeming "system" they're just aching to sell you in the form of some "method book," or whatever. But it's really just about as simple as Dan Haerle suggests, at least in his book *The Jazz Language* -- know the basic tools for creating melodies.
What I recommend is simply to transcribe, with pencil and staff paper, as many complete solos as you want, without worrying about a goal of playing them verbatim, and taking advantage of any technology you like (the "old" masters used to slow down records, as I did with reel-to-reel copies, so don't listen to people who say you shouldn't do that, if it helps, and it will for fast solos). You'll start seeing how things fit together.
Jazz-specific techniques? I can think of a few -- one is already demonstrated above in the video, namely, walking a LH bass. I don't walk LH much anymore except on Hammond organ, but I think pretty much every jazz pianist could do so for any tune if desired, meaning, improvise a walking bass and improvise over it. Other things? In theory, you don't really need to use a lot of sliding in semi-tones if your fingering is solid, but in practice, it's done all the time. Since you will be playing a lot of blues, even in non-blues tunes, it's pretty natural to use clusters of notes (or least, in Bb, something like a figure which has a G on top and some combination of Db-D below, for starters), so I would take advantage of that aspect of the idiom.
Oh yeah, the one aspect where if you must have a book besides Dan Haerle's for reference and the one every jazz musician makes for himself or herself (even if not written down) by transcribing from records) it could make sense is in Arranging. I can't remember which ones I've liked, but knowing standard voicings (like drop-2 or just general block chords) from the perspective of an arranger shouldn't hurt. You can take these off the record, of course, but just suggesting as an optional view from a different side.