How long is a piece of string?

Seriously, it depends on several factors (insulation of the bedroom, windows, facing direction, outside temperature and humidity, size of the mini). If the mini is correctly sized (ie taking into account of all those other factors), you're probably looking at a couple of hours, at least.

If the mini split was sized properly for the heat load of the room (considering all heat load sources) it wouldn't take that long assuming the mini split was installed propery with proper charge etc / working properly.

I would think you would start feeling the difference within 15 minutes and continued improvement with in the span of an hour.

How fast it gets to your desired set point depends on a long list of variables with a large part of that variable being how hot it is outside / how hot it is inside and how fast that heat is being exchanged from the structure you are trying to cool.

Only takes a spell to cool it down.