Any good suggestions for muting the D string? I notice that often while playing the D/G strings that I'll hit the D/G strings after playing a string. So, when I play a G, I'll bump the D and while playing a D, I'll hit the A string. I would classify this is hitting the string on the 'followthrough' to the string above.

I don't hit the strings while playing slow, but when I get up to speed I definitely hit them. while I'm working on not hitting them, i'm looking for a way to mute these two middle strings. (E isn't a problem as i always rest my right thumb on it)

Thanks

Could use the Floating Thumb technique, I beleive the thread with videos is in this section somewhere, you could try searching Floating Thumb. Hope it helps.

if you are using a 4 string, there is another technique that you can try. Assuming that you only use your index and your middle finger to pluck, you could use your pinky to mute the A string and the ring finger to mute the D string (or the other way round, whichever is more comfy for you). The thumb as usual stays on the E. But as soon as you move up to 6 strings or more, you'd have to somehow grow some extra fingers or use the floating thumb method.

I have always used floating thumb since I started, it just felt natural to me. Using this technique will definitely help to solve your problem.

I think you just need to work on your resting strokes for faster tempos.