How can I tell when wine has finished degassing?

One of the most simplest, inexpensive, and fast ways to degas wine is to buy a metal paint mixer at Home Depot for $16. Stick it in a battery drill and spin that wine, after racking to secondary of course, until it practically foams over. Takes about six seconds.

You probably have malolactic fermentation happening in the bottle. Apples are high in malic acid. If any oenococcus got in there-- it's ambient and lives in wood, often found in barns, garages, etc-- then it will eat the malic acid and produce lactic acid-- which is what makes Chardonnays buttery. The bacteria lives in oak, and is why we associate oak aging with buttery flavors in wine. It would be nice in an apple wine, so you might actually want it... but you need to let it complete it's process.

The solution: get an ML test kit from Vintner's Vault so you can test for completion and either (1) inoculate for ML fermentation by buying an ML culture and pitching it right after primary or (2) hit the wine with 25-50ppm SO2 after primary and 40ppm SO2 prior to bottling to lessen the chances of ML occurring in-bottle. Either way, you want to let the wine sit in tank for a few months before bottling, at least (if you're not oak aging it).

When I make a Rose, which I don't want to send through ML, I keep it in stainless until February or March or so, and then hammer it with SO2 at bottling.

I haven't done a whole lot of degassing of wines myself, generally if you let them bulk age long enough they degas on their own (which is what I usually do).

Here's an article on degassing that may be informative: http://homewinery.info/viewarticle.php?id=46

It sounds like you needed to do a lot more stirring to degas your wine.

I've also heard of people using a vacuvin to degas their wine, but that can take a long time.

Another thing you might want to try to improve your apple wine is to sweeten it. As long as you have added sorbate you can safely add sugar back to your wine and fermentation won't restart. dissolving sugar into the wine will help undissolve some of the CO2 as well as help cover up other off flavors that may be in the wine. Of course if you don't like semi-sweet or sweet wines, don't do this.

I don't think that a bubbly surface and harsh taste is a signature or inadequate degassing. If the wine fermented out to a 12% alcohol product, then fermentation was pretty good. The yeast would have consumed much of the O2 in the wine after pitching.

Perhaps some of the off flavors then is related to fermentation temp or the must itself.

I don't know a lot about making Apple Wine, but what I know of fermentation itself I can't imagine that degassing is the problem connected to your symptoms.

But I am open to criticism through voting and comments, I could be wrong.