I've been doing the bleach solution (1 tablespoon per gallon of warm water)
since I started brewing and I have never had an infected beer. So in terms
of sanitation, that seems to be working fine.

What I do think I am getting are off flavors from the bleach.

Here is my procedure:
I sanitize my carboys for 30-40 minutes with this solution and then rinse it
out with cold water and allow to drip dry on my carboy stand on top of a
clean kitchen towel.

I use the same solution to sanitize my bottles using a pump spray attachment
to my bottle tree. Three squirts and I let the bottles drip dry. These are
NOT rinsed, though and when I am ready to fill, I just shake out any
residual sanitizer from the bottle and then fill em up. Should I be rinsing
out my bottles, too?

What do you use to sanitize?