I don't use tea bags often (mostly when I'm traveling), but I usually find they're only good for two steepings, if that.

Green tea in bulk is good for three cups at least, sometimes I'll squeeze out a fourth.

Plus it's way cheaper, and you don't have to pick out those little wet staples before composting.

My mom tells me that historically, in China, those who could afford it would just throw out the first steeping, sometimes the first two, and drink only the second or third. Not me though!