I expect that how much time is required to learn the URB varies widely. My luthier told me when I bought my URB - 10 years. Through the years, I think I've found that there are times when I needed to practice a lot, particularly in the middle and these days. Less in the beginning. In the beginning, my strength wasn't up to the task. In the middle, my strength was, but I wasn't efficient yet. I spent a year mostly playing Major scales 2 to 4 hours every day, at first, to a recording, arco, 2 octaves, than 3 octaves, different fingerings, and eventually my ear was good enough to catch my intonation issues without a recording. 2 to 4 hours per day, for a year, just to get barely competent on the instrument. I'm STILL working on nailing thumb position! I embraced that task based on a recollection from David Friesen who said that that's how he learned to intonate properly. Taking David's advice moved me up an order of magnitude as a jazz bassist, IMO because I learned to "hear the pitches" before I play them and developed a sense of where those pitches are on the instrument. Those exercises made me fully know the fingerboard, nut, middle, above the octave and at the end, and that improved my playing an order of magnitude because I no longer needed to reach to the nut for many pitches as I heard them in my mind's ear. It taught me something else too, and that's efficiency. I learned to press "just hard enough with my left hand but not harder" - credit Rufus Reid with insight and I discovered that a lot of issues with TP were poor left hand commitment and pressure and not the bow.
When I screw up, it's most commonly because I don't place my finger where I heard the pitch. It's less than 10 percent of the time and almost always when I'm soloing but
@Chris Fitzgerald commented once about thumb position on the URB; to paraphrase "go for the pitches not the graphic diagram" and I have found that to be brilliant advice. Whenever I go for the pitch rather than an interval, even if I'm slightly off, I adjust quickly and the next note is in tune.
I don't know how many years it will take you to master the URB, actually, no one does, but, I do know that it will be measured in years, not months. And in terms of effort, effort-years, not effort-months. 20 minutes a day will not likely get you to your goal. Your existing musicianship will help, but will only get you partly there. Sheer repetition and careful analysis of what's wrong will get you the rest of the way.
Finally, teenagers find it easier than us old farts, so there's that.