I'm a rank newbie too. Took my second lesson yesterday.
I like to relate learning to play bass to anything else that requires skill. I'm an avid motorcyclist. I started riding seriously about 9 years ago. It took about three years of regular riding before I was really comfortable and never had to think about the motorcycle again. I just rode from "feel". I knew what was going on based on how things felt or sounded. From there, things really opened up. I took some racing classes, put lots of miles on the racetrack, and eventually reached a point where I am a very good, competent rider. I'm not the best, nor will I ever be. But riding is one of those things where if you push too hard, you end up hurt or dead. You have to stay in your comfort zone and take little baby steps. You can't go right out and drop a knee at 120mph. You have to first take the proper line at 50mph and learn the technique.
I feel playing the bass will be the same way. I'll spend years thinking about every note I play. Worrying where I put my fingers and constantly struggling to use proper technique to avoid developing bad habits. Then at some point, the light switch will come on and I'll say, "Humm, I just played an entire song and never once thought about my hands. I just played what 'felt' right".
I don't know exactly how long it will take to get there, and at this point, I know it's a long way off. I sit and play scales for hours. Resisting the temptation to go on You Tube and learn a slap technique or something beyond what I'm ready to play. I want to keep in mind those baby steps, and that there are no short cuts. It takes lots of practice.
The main thing for me is that even though I can't play a song, can't jam with a band, can't even think of gigging right now, I love the feel of my bass. I love the sound it makes. Nothing thrills me like a deep full note that rattles things in my house. Even if it's just scales or excercises at this point. I do little things like put on a drum track in GarageBand and play scales to a rhythm. Anything to break up the monotony and make it fun while still practicing what my instructor shows me.
I am starting out on a 5 string. I love the long B string. Love players like Jimmy Johnson. Even though the learning curve is a bit steeper, I am willing to put up with it to get comfortable from the beginning with that B string being there. Learning the "wandering thumb" technique and having to work around that low string. Getting my hand stretched out to cover all four frets on that string starting at the first fret. I have huge hands, and it's still not easy, but I keep at it so I can develop my "stretch".
I used to play basketball, and I had a coach that used to run the first few practices without using any basketballs. We worked on footwork, offensive and defensive movement, communication, picks, and other things that didn't require the ball. To me, the "ball" is the music. Before you can make music, you need to have all the fundamentals in place. How long will it be before I an pick up the ball and start playing? I don't know. My goal is to be able to play well enough to jam with a group of people within a year. Not to gig mind you, just to be able to confidently play root notes or roots, octaves, and fifths without fouling up too much. In two years I hope to be able to play in my church band. Goals are important to me, and I think those are attainable goals.
Within 3 years, I hope to be playing entirely from "feel" without having to think about where notes are on the fretboard or what string I'm plucking etc.
When I practice, I try to put in at least an hour. That's not always possible and I travel a lot for work, so practicing every day is not possible. Because of this, I know it will take me a lot longer than someone who has lots of free time.
In the end, it comes down to the fact that I've loved bass since I was a kid. Loved the sound. Loved the "feel" it adds to music. I'm looking forward to being a lifetime learner.