Nice layer of foam on top usually means its still doing something. (If) when the bubbler stops bubbling, use a hydrometer and a sanitized wine thief and see if its done (at least in gravity range for the style). If it is close to your expectations, test again the following two days. If it doesnt move over the course of a few days, its done (which might be a little late to completely deal with oxygen introduced during the transfer.. careful handling can minimize this)
Im assuming you dont have a CO2 tank, nor the ability to crash cool. If you are almost done (or done done), you could just fill the secondary container with CO2 and not have any real worries about oxidation. You could just crash cool to ~34°F for a day or two to clean it up and not really need a secondary. I dont do one anymore unless I dry hop or I make a fruit beer.
If you really need to secondary, Id wait till its almost all the way done (within a couple of points of your desired finishing gravity) and try not to make bubbles when transferring. The remaining yeast in suspension can consume the oxygen that youve introduced; just dont take it off the cake until youve gotten close. A stopped bubbler doesnt necessarily mean anything.