Hello fellow lengthy bath lover!
There are quite a few waterproof wireless keyboards and mice out there, or you could get a waterproof wireless keyboard that includes a trackpoint or touchpad. Connect it to a computer outside the bathroom. That's half the equation. Then you need something to look at. There are several options:
You could go for a waterproof bathroom TV - this one is heated, $400 and includes a Fire stick though there might be others cheaper. This might require wiring in, though it's IP65 and safe to use if it's done properly. Wish I could have one but my other half would never allow it.
http://www.bathroomtv.co.uk/smart-bathroom-mirror-tv-19inch.htm
You could go for a waterproof ipad cover, which are quite cheap, and get a second hand ipad to put in them.
https://www.google.co.uk/search?q=waterproof+ipad
If you go this route then you'll need a bluetooth waterproof wireless keyboard to connect to the iPad. Some of the flexible ones are truly terrible, I know I've tried them and recoiled in horror.
The ghetto solution would be to get a cheap TV or monitor, and put it behind some glass or in a perspex enclosure near your bath. They should cope fine with some damp air or a bit of heat. And if they don't, they're only a few dollars to replace. However, you'd be breaking multiple safely regulations just having it in your bathroom, though I don't think it's actually illegal as long as you are the only one using it. If you put it in, and another person uses it and is harmed, you're in for the chop.
(whisper: I've been known to put my laptop / ipad on a stool near the bath and watch a film in the bath that way. I figure if they can work in tropical humidity, then they can survive two hours in a moist bathroom. No problems so far ...)