Hi and welcome to the forum.
One way to avoid shocking your betta with too much fresh or different water is drip acclimation. The idea behind this is to slowly acclimate your fish to any differences there may be in the water of his current home and the water in his new home. Temperature, chemistry etc, those kind of differences. First, fill up his new tank with conditioned water and get it running the way you want. Next, empty his 1g bowl about halfway. Now, there are two ways to do this.
One is to take a length of thin airline hose. Put one end in the new tank and suck on the other end to get a siphon going. Once the water is flowing, try tying a knot or clamping the hose so that the water flow is reduced to a few drips. Put the dripping end in his bowl with him. At this point, all you can do is wait. When the volume of water in his bowl has doubled or so, you can net him and deposit him in his new tank. I personally never could get a knot tight enough to slow the water enough but it could have just been my airline hose.
The other way is to scoop up water from his new tank into a pitcher or bowl. Every ten-fifteen minutes or so dribble just a bit of this water into his bowl with him. Repeat until the volume of water has doubled and you can net him and deposit him in his new tank. For future reference, use drip acclimation any time you bring home a new fish. It reduces the stress on the fish and means it has a greater chance of surviving the move.
Now, to be honest, I would continue the aquarium salt treatment in the 1g bowl. With a salt treatment, you'll have to change the water every day and redo the salt and it's just easier to do in a small bowl. But that's just me.
If you don't mind changing a little more water every day, then you can transfer him to his new home and let him get used to it for about a day. Then you can add the salt. It's 1 teaspoon per gallon.
Oh, another thing. Does your new tank have a filter with it? Then you'll want to do the salt treatment in the 1g bowl because the salt could delay the biological cycling of the filter. In a 2.5g tank with a filter, I'd suggest changing 50% of the water once a week and 100% with a gravel vacuum once a week.