I'm trying to make things a bit more sanitary in my winemaking process, so I
bought myself an auto-siphon. A 3/8" I.D. hose fits over the pipe coming
out of the auto-siphon, a little loose for my taste, but a 5/16" I.D. hose
will not fit.

So, my issue is this: when in use, it seems like a lot of air stays in the
hose and I can see bubbles all along the length.

The solution I've tried so far is to just have a very short length of 3/8"
hose at the end of the auto-siphon, with a long length of 5/16" hose crammed
into the other end. When it works, it seems to drastically reduce the
bubble problem, but I do seem to have trouble keeping it going.

Any suggestions?