With an hour's practice a day, your bass in hand, things will go pretty quickly, but it will take several months to be able to look at a new piece of music and read it straight away.
There are different aspects to reading, such as rhythm and pitch, which you can actually work on separately.
Use a metronome to practice your rhythm reading. Learn what different groupings sound like, especially in 8th and 16th notes.
Don't forget you can slow down any rhythm with your metronome, so that you take each quarter note in a measure and treat it as four distinct beats.
An arpeggio ... 1 3 5 7 8 will have a distinct shape when written out, as will an ascending or descending scale. Try "Bass Guitar Exercises for Dummies" It will get you playing scales and arpeggios and recognising what you have to do, the muscle memory being linked to your eyes. Your ears will tell you if you're in the right key.
Don't forget to look at the key signature, and position your hands on the E and A string accordingly.
If you start out ready to play Bb, then the patterns you see on the stave will fall under your hand; The spaces are a third away from each other, as are the lines.
Get a book of simple melodies, like Christmas Carols, Nursery Rhymes, 100 Cowboy songs, which are written in treble clef, get some music paper and transpose it into bass clef. There's nothing like actually writing notation to help you learn to read it. You also learn to read treble clef at the same time.
Get some bass tab, starting with simple grooves, and write it out as musical notation in bass clef. You know that "7" on the A string is an E, and you know it's not the lowest E, so you learn quickly where it is on the stave.
When you make up a groove of your own, write it out.
Listen to peces that you know well and can play without too much difficulty with the sheet music in front of you, and follow the bass, doing the "Boom boom boom boom boooom bum bum" thing, tapping your feet and nodding your head. Try to recreate that afterwards without the song playing, just reading, tapping and "boom booming".
There are apps for i-phone etc which are like flash card games. You see a note written out and have to tap the fret on the fret board, or variations thereof.
It's all good, and eventually you'll wonder what seemed so difficult.