Hey,
The bacteria isnt actually in your water, it is in your substrate (gravel) and in your filter so i would doubt just adding aged water from your old tank would add bacteria.
I actually just bought a new tank two days ago 30 litre tank and added about 2-3 litres of water from my old tank and 20+ litres of new water with water conditioner added but i added all of the gravel from the old tank to the new tank and also just put the old filter straight into the new tank, i tested for ammonia and after 2 days its still at 0.
My advice, add your gravel and your filter from the old tank to the new without washing either of them then check the ammonia levels for a few days.
Or if your still going to use your 2 ft tank add a handful of gravel from your old tank to your new tank which should speed up the cycling period.