I am 18 and I would like to learn piano. I’ve played clarinet in a school band since I was 10 so I know everything about timing and I can read treble staff in sheet music (not bass though). I started teaching myself with a beginner’s book for adults and I’ve been practicing about 20 minutes a day for almost a week now and I am just starting to kind of understand the bass staff. If I keep up at this pace, how long until I can play considerably well? (Like good enough to play for other people’s pleasure at family events and stuff, I guess)
It's impossible to say. Given that you played clarinet in a school band means your treble clef reading should be pretty good, so it's a head start.
Learning to play an instrument is divided into two tenuously linked parts. One is the music itself, whether it's tadpoles on washing lines or listening and trying to repeat what's heard. Two is the instrument itself. How it works, the geography of it.
You have part of the first, although reading and playing two separate lines simultaneously is new to you, as is producing several notes at the same time - not easy on clarinet.,
The second part is finding your way round the piano. Very different, but made simpler by a fixed repeating pattern (Don't all patterns repeat?). Being able to play multiple notes together, with one or two hands.
I guess, since you already read, you'll go down the path of using dots. However, how long it'll take to get proficient is anyone's guess. How long did it take you to get proficient on clarinet? Bearing in mind the reading is easier, generally? There's the figure of 10,000 hrs bandied around. You may be one third of the way there, so maybe the answer's around another 6,000 hrs...
At an hour a day, that's 16 years left ! Again, how proficient is proficient? And how effective is your practice time? How good at retaining knowledge are you? When will you realise a teacher is needed? So many questions!!
Even "good enough to play for other people’s pleasure at family events and stuff" is a fairly arbitrary level but I think it's possible to give you an idea.
You can take normal curricula like ABRSM or RCM as a baseline. They have a system of grades or levels each with a repertoire assigned to it. My experience is that you can read those grades or levels as "schoolyears" of an average student starting as a child, who regularly practices (= almost daily). So this means as well that daily practice time should increase while climbing through the grades (grade 1 starting at 15 minutes, grade 5 repertoire requiring let's say an hour of daily practice time and grade 8 maybe up to 2 hours). This gives you a certain scale of what is required for your goal.
If you look up the music belonging to each grade you'll get an idea of what each grade means. You'll notice that there is quite nice music also in the early grades (not only nursery songs). If you want to play more popular songs, there is a lot of sheet music advertised as 'easy' which can mean anything but normaly means around grade 2-4.
Of course you have a considerable head start by being able to play another musical instrument. You are able to practice, read music, have musical insight (about phrasing for example). So you can move quite a bit faster through those first grades.
So my answer is: if you dilligently do your daily practice you'll be able to progress in such a way that in one or two years you'll be able to play some pleasant songs and pieces at family events (It won't be Rachmaninov though :-))