Hi! That's a big, good looking plant you've been given. I've managed to bloom my medusae successfully three years in a row now. Everyone's growing conditions are different, but here's what I do:
I grow it in a teak basket, in a 50/50 mix of NZ sphagnum moss and shredded tree fern bark. It seems to want to dry out a bit more between watering than my other Bulbos, so I usually wait til the surface of the moss is dry to the touch, almost "crispy," before watering; might seem too dry, but bear in mind that there will still be a good amount of moisture underneath, where you can't see. Also, try to keep the water from collecting on or around new growths, as they can rot easily if they're constantly wet. (And that's true for all Bulbos.) I feed it with a really weak MSU mixture about ever two weeks during the growing season.
As far as light, the basket hangs six inches below a bank of T5 lights, but I have a mesh screen right below the bulbs to cut down on the intensity. The plant also grows toward the end of the fixture, where the light isn't as strong. I have a fan running all the time to help with air movement.
Hope some of this helps!
Bulbophyllum medusae 'Orchidglade'
That a beautiful size medusae. Mine has been busy putting out new growth all summer. Have it in bark with CHC on top, in a net basket. I was watering this one every day throughout summer and have begun to cut back to about every 3 days now. It's on the patio in still, very hot conditions but, not nearly as stifling as it has been so, watering less now. These adapt very quickly to the baskets and half the new growth is creeping through the slats. Why would you want to divide yours? It looks great now and potentially, a specimen medusae if you keep it as is. (Just a thought... 
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I'd love all my stuff in baskets and hanging all over the place but just isn't in the cards just now...but someday when I REALLY get sick of winter's nastiness and relocate to a warmer situation....
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