I can't recommend this book highly enough for someone learning to read standard notation. For someone like you who already has the mechanics of playing it will be a breeze. However, try not to fall back on old strengths of using your ability to memorize bass lines -- actually *read* each exercise as you play along. Don't move to the next page until you can get through the exercise, then move on. In a few weeks you'll have the basics down.
Ed Freidland's Bass Method
https://www.amazon.com/Leonard-Bass-Method-Easy-Use/dp/0793563836/
Since you read tabs, you are probably already familiar with the Ultimate Guitar website. What is new is there is now an option for viewing songs in standard notation, with or without tabs. This feature is only available on the "official version" transcriptions (ones they have created themselves) and that requires a $5/month subscription, but that is not much for music education. Find some songs you like and learn them by reading the transcriptions in standard notation. Maybe at first enable the tablature feature as a crutch, but use it only if you get stuck.