Agh, I'm moving this week - with five tanks..
I feel for you.
If you dip the cup in the water, you'll notice how the water gets sucked into it. If you feed your fish and kind of sneak up behind him with the cup, dip it in gently and let the water suck him into the cup, you'll find it much easier than chasing him about the tank with it.
To move my smaller (10 g and under) tanks, I'm cupping the bettas, draining the tanks (they're planted, so I don't want to take them apart if I can avoid it), sitting the bettas in the cups inside the tanks and carrying each one over on my knee.
Luckily, it's not far to go (10 mins away), and it won't take long to set each tank up at the other end.
If it's warm weather there, your fish ought not get too cold.. might want to ensure he won't get too hot in the cup, though, in the car. Little cups get hot/cold really rapidly.
It's the 3-foot tank I'm not looking forward to. My wilds, Darwin shrimp and snails are moving into a 15 g plastic tub with a heater and a pile of moss for a few days, until I can get their tank over in the moving truck. If it happens to get broken by the movers it'll be covered by insurance and the fish will have somewhere to be until a replacement can be organised.
Moving with fish is the suck. I feel for you. Hope it goes well. :)