Don't know if besseae will be dramatically different from other phrags, but in general phrag flowers don't last as long as paph flowers, so you don't have as much time to think about it.
The issue isn't so much the age of the pollen as the age of the flower being pollinated. In the thread that NYEric listed there is a post from Leo on how he used stored pollen to make crosses, so viable pollen can be months old, but you need to get it into a fairly fresh flower.
I spent allot of time getting pearcei pollinated. When my greenhouse was dryer (humidity <60%), I couldn't get a pod started no matter if I opened a bud just before it did it itself. Probably well over a dozen attempts. But after raising air humidity into the 70 and 80% range almost every attempt took even if I waited 5-7 days after the flower opened (about 6 attempts).
By the time I tried wallisii my humid air climate was well established, and I can self a mature flower, and the pollination will usually take.
