I learned to read music long before bass guitar ever entered my life. So I have solid comprehension and understanding of keys, scales, etc.
First, good for you OP for wanting to become more of a musician - I believe most don't really go there. They figure it out in other ways and don't worry about note values. Fact is, as you've already discovered by using tabs, you don't really need to to get by. And this has always been the reason I'm not a fan of tabs - it takes the music out of music. I'll not argue that they have no place - I have used them to figure out a couple of fingering options. But for a lot of players, that's where they stay.
Having said all that, I find that when I'm playing something I know, I don't think in terms of notes, rather in terms of patterns or in intervals. I pretty much only use note names (in my head) when learning new stuff. When I first started learning bass, and got into learning the fretboard, I used patterns to help ID notes up the neck. There's no reason you can't do that to learn your note names.
As previously suggested, start by learning the notes of your open strings. Then you can establish the relationships between them, the notes between E and A for example. Do this for all the strings. Formally trained bassists tend to live beneath the 5th fret for a long time and that's where they learn the notes. I'd suggest you start there too. Once you have the first 5 frets dialed in, move up to the next 5 frets. You'll quickly start detecting patterns and you'll probably find that the second 5 frets comes very quickly. Keep moving up until you run out of fretboard (or at least up to the 12th fret).
A second concept would be to learn all the notes on one string (say the E string). Once you do that, you can start interval hunting (finding where the octave of each note is, then finding (and identifying) the 5ths and 4th, eventually all of the intervals. Once your comfy on the E string, do it again on the A string, and again, you'll quickly recognize the patterns and it comes more quickly.
I can't recommend any books, but I would thing that anything that does introductory bass lessons will get you started. I'd bet there are plenty of YouTube videos that go over this as well. They may not cover the whole fretboard, but once you get a basic understanding of one section, the rest is just pattern recognition.