Dre my advice (same for any instrument) is to pick some songs you like and learn them, even if they seem like they might be a little too hard for you now. Do this in addition to practicing scales, chords, finger strength, and stretching. Make sure that you keep your elbow separated from your body so that your left wrist is nice and relaxed. That’ll keep you from getting serious problems later.
If you pick songs that have a technical aspect of playing that you aren’t good at, for example a slide, bend, trill, muting, etc., it makes it easier and more fun to learn than if you’re just learning the technique by itself.
Specifically for speed, there are two types of drills that you can play around with. Which you prefer may depend on the kind of music you like. If you want to shred, I highly recommend trying to learn a song like Master of Puppets. It’s fast but the riffs aren’t very difficult once you get decent at speed.
One drill is to alternate rhythms on a single string with each or alternating fingers. Pretend this is a tab:
E: |1 0 2 0 3 0 4 0 1 0 2 0 3 0 4 0 
Start slow and build up speed. It’s good to alternate off the E so you can practice getting a good note when you’re hitting stuff at a faster tempo. Then you vary what you’re playing in two ways. You can jump strings and practice your finger work that way - for instance a progression like E A E D E G etc. or change the rhythm by adding root notes:
E2: |1 0 0 2 0 0 3 0 0 4 0 0 1 0 0 2 0 0 3 0 0 4 0 0 
E3: |1 0 0 0 2 0 0 0 3 0 0 0 4 0 0 0 
So in E1 you have an 8th note feel to the riff, E2 is a triplet feel or 12/8, and E3 is a 16th note feel. If you are in to metal, you will hear these kinds of progressions all over the place in most thrash bands.
The other method I would suggestion is a bit simpler. Pick any riff you like and start playing it at a slow pace. Gradually accelerate the tempo until you get to a point where it sounds like shit. Focus on making every note clear and crisp as you go faster. Once you break down, restart at the slow speed and build up again. The crisper and more distinct you make the notes, the better you will sound, especially if you ever play distorted.
Gotta build up muscle memory in your fingers and hands just like you do for lifting 
For background, I played jazz trombone for about 10 years, and taught myself bass 4.5 years ago and I play in a metal band now.