Well Sara-s - I am told it is a Bonzai Ficus Cera. I have got it on my window sill (in the sun when the sun comes out here which is not too often!) in a centrally heated house. If I open the window I will move it so that it is not in a draught.
First, a bit of nit-picking from a spelling nerd; it’s Bonsai. “Banzai” is a Japanese battle cry.
Ficus is a tropical plant, so it’s fine indoors. You can put it outside in the warmer months. Keep soil moist, but not drenched. Since it is a tropical, it should be misted regularly, as central heating makes air very dry. Look for some plant food that is meant for tropical plants.
Also, check the surface of the soil. Some vendors will glue a layer of rock to the surface, to make it look pretty. But that impedes water absorption. If that is the case, just peel off the rocks.
If you could post a pic, it would be helpful.