When I play, I always seem to rest my thumb on the string above the string I'm playing on. I've noticed basically everyone keeps their thumb resting on the pickup. Is my way poor technique? Should I practice to make myself keep my thumb on the pickup?
If it's not hurting your playing speed or your thumb I really don't see a problem. It's more personal preference then anything else. I prefer to rest on the pickup or the thumb rest, but more often then not I just use a pick.

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no i do this too. its fine i wouldnt worry about it if its comfortable then keep doing it.
yeah, i do that sometimes too, but only when i feel really comfortable playing the song. i usually rest my thumb on the front pickup of my jbass, everybody says its wierd, but ive done it since ive been playing and no one told me to. its just natural for me.
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Well that makes me feel better. I can play faster when I do this. I was just wondering if it was kind of odd i guess.
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Well that makes me feel better. I can play faster when I do this. I was just wondering if it was kind of odd i guess.

Nope that is what is called a floating thumb technique. Perfectly acceptable and not odd at all.
Actually, that's just about how you are supposed to play. 'Proper' technique is when you are playing on the E or A, your thumb is on the pickup. On the D, you rest your thumb on the E. On the G, rest your thumb on the A and press it against the E as well. The reason for this is so your thumb mutes the other strings that you aren't playing on, and your fingers will mute the string directly above it on the followthrough when you pluck.

My instructions are on the assumption that you are playing a 4 string, but you get the idea, adjust as needed.
^ I wouldn't say that's proper technique. It's a technique but with thumb resting it's pretty objective. This way I've found my thumb sometimes got tangled up in my playing so I switched over to the only on the pickup, but if you're not worried about it be my guest.
I used to do it, then I got sick of having to move, so I leave it on the pickup.
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EDIT: Sammcl pretty much got it dead on.
my thumb moves from pickup to E string when im playing the bottom 3 strings, i dont even notice it move, it just moves naturally
I occasionally play like that, but more often than not I stay on the pickup. I find it easier, I'd have to think about moving it.
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a good rule of thumb (so to speak) is to only rest it on the pickup or the E string, never on the A or D strings. This cramps up your hand and can slow you down.... unless you have really tiny hands.
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