The best way to get better is by playing jazz. This is especially true once you are past the fundamentals like scales as it sounds like you are.
Patterns
If you want to brush up and take that further I'd look into arpeggios and "patterns" (link) (link) (link). That is, playing arpeggios and their extensions from and to various scale degrees, as well as other idiomatic melodic patterns. These can help generally with technique just as playing anything can but more importantly the idea is that getting these under your fingers will make them slip into your improvising. This same concept applies to stealing licks from your favorite records—it's about building your vocabulary.
Theory
You can also always dig deeper into the theory and various approaches to improvising. For instance if you aren't familiar with things like guide tones, target and approach notes, enclosures, sequences, etc, they will all help. You can usually always dig deeper into your harmonic approach as well. You said you know "major, minor, and a few different scales", so it sounds like maybe you could dig a bit deeper into modes.
As far as a theory books, maybe check out Mark Levine's "The Jazz Theory Book" and/or Bert Ligon's Jazz Theory Resources. Andy Jaffe's Jazz Harmony is decent too and quite a bit shorter. There are all kinds of other books that either get more advanced or dive into specific topics. No single book will get you everything but a general theory overview book is a good start.
Playing Tunes
But as much of possible of this should be done in the context of tunes. Get some fake books (ex. The Real Books or The New Real Books) if you don't have them already and start working through tunes. Play the head and then a few choruses of improv just like if you were performing the tune. Dig deeper into the changes of these tunes and analyze them. Try different scales, modes, superimposed arpeggios, and patterns, etc. The point being that you should work new things in but the bulk of your practice time should be put toward actually doing what you're practicing for ... playing jazz.
Accompaniment
Jamey Aebersold's Play-Alongs are great for all this because they are focused around playing some tunes, have accompanying backing tracks, and include a book that gives you some things to work on within the tunes.
But something like Band-in-Box that can play whatever changes you put in is really useful either way.
Alto-specific
I don't think there's much alto-specific advice because the concepts are largely the same for all instruments with the exception that you don't have to worry about about playing chords like a piano or guitar player would. Though it's pretty common for students of any instrument, it may be particularly salient for an alto player to study the work of Charlie Parker. Even his heads are a good melodic exercise and embody the bebop sound. And because so many other musicians were inspired by him and studied him, it serves as a bit of a prerequisite to most of the jazz that came after. "The Omnibook" is worth picking up.
Listen
And of course, always be listening to jazz. Try transcribing things you like. Then study them, alter them, an work them into your solos.
