I tried the method of using bleach and hot water as directed but after three applications there is still a faint odor.
Any other suggestions?

Are you getting the smell from the drain or the disposal? Cheers, Tom

The smell is coming from the bathroom sink.

The smell is coming from the bathroom sink.

Let's get together on plumbing terms.
Sink= kitchen sink
lavatory=bathroom sink
Now on to your smelly problem. Remove the stopper from your lavatory. Look down in the drain and you will see a rod about 6" down. Hair hangs up and fermemts on that rod. Fish it out,(ugh!) The reason you smell it at the overflow is that when you drain some of the smell is forced back out the overflow. Now pour a quart of bleach down the drain and let it set overnight. Next morning,(and this is important)flush it out with a pan of boiling water If you can't pull the stopper out then your stopper has a opening at the base that the rod goes through so that it can't be pulled out. To defeat this and pull the stopper look under the sink and follow the pop up lever down to the rod. You will see a knurled nut. Now push the pop up knob so the stopper is in the up position. While holding the stopper in one hand, slowly back the nut out until it's clear,(You may need to free it with a pair of pliers) Careful! You don't want to pull it all the way out. Now, GENTLY pull back on the rod while pulling upwards on the stopper. As soon as the stopper clears turn the nut back in hand tight or tight enough to hold the plunger rod up. From here on in you will let the stopper ride on top of the rod instead of tying it down. Now take a bent coathanger and fish out any hair that may have hung up on the rod or the trap. After you have cleared out any hair or trash, just drop the stopper back in the drain. When I install a lavatory I never tie down the stopper so that the owner can check the drain without the expense of a service call That should take care of that smelly lavatory. More questions? I'm as close as a click. Good luck TOM