How long should I let my beer sit out before bottling after cold crashing? How long does the yeast need to "wake up"?
You really don't have to wait at all. The yeast will 'wake up' when the bottles warm toward room temp in the presence of the priming sugar. Edit: Guess I should add... if you had to move your fermenter to a different place for bottling (like from a chest freezer to a table top), you'll probably want to allow whatever got stirred up by the movement to settle before you bottle.
I think moving the fermenter would defeat the purpose of cold crashing entirely. I'd also pitch some fresh yeast to ensure it didn't all floculate out. Insurance is so much easier to deal with than 50 flat beers.
When I've cold crashed all of my yeast has completely fallen out of suspension and went to sleep making it necessary for me to pitch fresh yeast as mentioned above. Otherwise it is likely you'll end up with flat beer and residual sweetness from the uneaten priming sugar - this is from experience with a wee heavy I brewed.
I never repitch yeast when bottling, never had a problem, even you cold crash your beer for a long time there will always be enough yeast remaining to carb at room temp.
Another consideration is residual CO2. Cold beer will hold more CO2 than warm. Assuming there is any activity (maybe not) when you cold crash, the beer will lose CO2 as it warms. Unless you can bottle and cap quickly, there will be differences in the residual CO2 from the start to the finish of bottling, if you try to do it cold. That's why carbonation calculators always ask for the temperature of the beer at bottling time. I usually allow my cold-crashed beer to warm to room temp for this reason.
If fermentation was down before cold crashing, I wouldn't worry about this. There's no more CO2 being produced to be retained as residual.