Reading music relies on a bunch of different processes. When you are first learning, you have to go slow because you have to deal with multiple processes on a conscious level. As you begin to master the instrument, many of these process become increasingly automated.
Let's say the written note is a C.
As a beginner, you have to consider if this is a C natural, C#, or Cb. To figure this out, you must consult the key signature. If the key is G major (one sharp), the C is natural. If the key is D major ( two sharps), it's C#), If the key is Gb major (6 flats), it's Cb. As a beginner you may have to stop and figure the key. As veteran player you should know the key at a glance.
As a beginner you need to figure out where to play the note. If you are just starting, this may involve identifying the A string and then counting the frets up to C. Optionally, you may have a reason to play the note on the E string, so you will play it at a different position on the neck.
As a seasoned player much of the process is automatic. You look at the key signature, and when you see a written C you intuitively know if it is C natural, C#, or Cb. You may need to consciously decide if you will play the note on the A or E string and which finger to use, but you probably won't have to think too much about which fret is the target. You see the note and just play it. While playing you don't necessarily even think of the note names.
The decision where to play the note on the neck is based on the shape of the bass line. In other words, where has the melody of the line been and where is it going. To do this, you quickly review and analyze anywhere between a few notes to a couple of measures of music. Once your hand is is position, you intuitively know which finger to use for the next notes in the music. If the music is fast, technical, and requires a shift, the shift may happen automatically or you may have to stop and figure how to play the line. You may stumble while sight reading, but later with practice the line becomes automatic.
While you are playing, your conscious mind shifts between several mental processes. Essentially the most important process at a given moment should rise to the conscious level. However, you don't necessarily use the same mental process for a give section of music every time. One time through you might be thinking about the note and the next time through you may focus on feel or dynamics.
Understanding rhythm and feel also involve multiple processes. As a beginner, you have to work through rhythms consciously to figure out the timing of a line. But as you gain experience, you see the notes and automatically know the correct rhythm without having to figure it out.
Learning to play is not a one and done ordeal. You proficiency will vary depending upon your most recent experiences. If you play a lot of music in Gb major, you will get really good at it. If you rarely play in Gb major you proficiency will decline unless you practice to maintain proficiency in the key. Same goes for rhythms. Rhythm notation for funk tunes looks a lot different than rhythm notation for classical music. So you be really good at reading funk and get totally thrown if you have to read some classical music.