I also had only acclimated fish in bags, not cups.
You could move him from the cup to the bag...that is an option.
We put our new Betta into our tank last Sunday - not even a week yet!
He was in a cup....here is what I did...
Floated cup in tank for 20 minutes (trying to warm him up because I could tell that cup water was cooler than my tank).
After that - I took out a little cup water, and put in a little tank water - all this while leaving the cup floating in the tank.
First time I did that I gave him about 10 minutes with the 'new' bit of water.
Then I took out some cup water and added that amount of tank water back into the cup....I repeated this several times and would let him hang out at least 5 minutes between taking out/adding in.
Every time I'd take out his cup water - I'd put it down the sink.
**I used new never-used, hot-water rinsed Solo cups for this process. One Solo cup was for dipping tank water, one for dipping out the old cup water.
The whole process - all the time with the cup floating in the tank - took about an hour.
We were putting him into a 5 gallon filtered tank with a heater - brand new set up.
When I cut him loose into the tank I also added half of the container of Dr Tim's One & Only (shout out to Hallyx for that suggestion - Dr Tims is my new favorite product).
So far - so good. All is well and daily water test results show everything at zero. Sweet.
Fish seems happy, eating well...acting fine...
I had the tank up and running a little over 24 hours when we brought the fish home too - make sure you do that so you know your heater is ok and all that.
I use Prime as my water conditioner.
I also have a thermometer in the tank - the kind that sinks and you just shove it into some gravel.
I got the Prime, heater, Dr Tims and some other stuff from Foster & Smith - I had enough for free shipping - they even put the Dr Tim's in cold packs - even with the free shipping.