When I was reading about batonnage (in a nearby post), the comment was made that after stirring, the CO2 generated by fermentation tends to keep particles in suspension. So, bernardsmith is pretty much on the money re waiting for the cider to self degas.
However, some years ago when I tried making blackberry wine (it was awful rather than awesome!) the recommendation was to degas before bottling. It was suggested using a vacuum cleaner sealed with tape around the top of the carboy, and it sort-of worked. It was amazing just how much the wine degassed, you could see the bubbles rising. Another "toy" was something called vacuvin used in the days before most wine bottles had stelvin caps. This was a little vacuum pump to use if you didn't finish a bottle of wine. It came with rubber corks that had a "slit valve" so if you pumped the air out of the bottle, the valve closed and stopped the wine from oxidising. Don't know if it worked because the wine never lasted long enough to oxidise for more than two days anyway.
Anyhow, the point is that with batonnage, the stirring degasses the wine and once the stirring stops, the particles settle out quite quickly because there is no longer CO2 attached to keep them in suspension.
I generally add pectinase at the start (I press my own apples so there is plenty of muck in the juice) and get a lot of settled sediment by the time fermentation has reached half-way. By the time fermentation has finished, the cider is usually quite clear and stays that way with careful bottling.