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I play tuba in jazz band at my school and I'm looking for a way to improve my reading of the in-staff music like the bass reads, and I thought a good way to do so would be to study in a trombone book. This is a bit unconventional, I know. Are there any books you guys can recommend? And if there's a better way to strengthen this reading skill, can you recommend that as well?

I used the trombone version of the Arban book when I was in high school. Reading bass parts down an octave became easy, and it turned out to be a useful skill. I also enjoyed trombone books of "everybody's favorite" type melodies. There are plenty of them out there.