For the majority of my bass students, learning to read musical notation is something we get to... eventually.
If there are no outside forces pushing the student to learn sooner, it can be eight or twelve months before we even talk about it.
I have no problem saying this in a public forum. This idea is no longer so heretical. After all, some very high profile musicians, bassists and otherwise, admittedly can't read music at all (Paul McCartney, Pino Palladino, Billy Sheehan, Duck Dunn, Rocco Prestia, Stuart Zender, composers Danny Elfman and Hans Zimmer, etc). However, I think that if any of these musicians felt the need to learn how, they could become very adept at reading in no time.
I see it as very simple: you learned to talk before you learned to read. If you tried to learn to read before you learned to talk, you'd have no "voice" in your head saying the word you'd be trying to establish an association with.
You need practice SAYING words before you can readily accept associating those words with symbols, and the same is true with notes on a staff. Dots and lines moving around on paper mean nothing musical to your brain until you understand pitch. Realizing how you as a musician control the creation of pitch with your instrument is key to the reading process, and having the judgement to know when you have created a pitch successfully is equally important. You need to be comfortable creating notes and listening to yourself as you play before you'll be able to pay attention to anything else.
Students who learn to read as they learn to play tend to experience the process very slowly and clumsily, whereas those who learn to read once they already know how to play tend to assimilate reading very quickly.
Broken down, the process of sight-reading music goes like this:
1. Eyes observe symbol
2. Brain translates symbol into music information and realizes options for executing this information as a note on the instrument
3. Brain decides how to execute, sends appropriate nerve impulses
4. Hands receive impulses and react
5. Ears hear resulting note and confirm or deny success of the action
Assuming the action was successful, that can all happen in a fraction of a second for a seasoned professional musician. For a beginner though -- someone whose experience with playing, listening, and reading is all negligible… this can literally take MINUTES. For every single note on a page, a student can experience an inner monologue something like this:
"What's that dot mean?"
"It means F."
"What's an F?"
"It's that note you learned on the third fret."
"How do I make it come out?"
"Press down like you're supposed to."
"Was that right? Did I press it down like I'm supposed to?"
"I think so. There wasn't much buzzing."
"Great. So was it the right note?"
"Well, I'm pretty sure it was on the third fret."
"But did it sound right?"
"I'm not sure. Was I listening?"
"Keep going; maybe the next note will make more sense."
"I had to look down for a second; I'm not sure where the next note is."
"Scan the page!… Scan the page!… ummm…."
…and on and on. When a student's hands and ears have not already been coordinated, adding the additional processes of reading and processing musical notation is exponentially harder, and this can be painfully slow and frustrating.
Make no mistake, performing while reading a piece of music means executing three cerebrally intense tasks at once: reading, playing, and listening. Before you can do all three simultaneously, you should be comfortable enough with two of them that you can put your attention on the third.