My secret is:
Yup, Mr. Clean Magic Eraser, or any other brand of melamine foam cleaning sponge. Here's how I clean my bottles.
I get out a Mr. Clean Magic Eraser Sponge,
Spend a few seconds peeling off what I can off the label,
Then I fill up the sink,
And run the label under the water.
Then I scrape the label with my thumb to get down to the glue.
This also gives more surface area for the sponge to reach.
Get the Magic Eraser wet,
And wash the label area, using pressure to get the glue off.
When finished before draining the sink clean all the label gunk out.
The bottle will be all clean! It takes about 2 minutes per bottle.
It will use up the sponge quite quickly, but it saves so much time peeling labels
that it's worth it for me to buy the sponges.
I hope this helps you complete your wine bottle project!