Hello,

I have a Bougainvillea bonsai that I'm trying to take care of but I'm not quite sure if I'm doing a good job.

I received it already potted as a gift around a month or two ago and have been watering it (mostly water from the tap) ever since by keeping the soil moist (not letting it dry out) when I can.

I keep it indoors and near a window with direct sunlight. (I can't keep it outdoors because it's too cold now).

It grew three new branches under my care but I'm not sure if the trunk is supposed to get thicker or if it's supposed to be growing more foliage/branches.

Any tips?

I've included a picture.

In one or two months there will not be any thickening that you can see my eye. In fact, with that small pot and kept inside there will not be any noticable thickening in a full growing season.

To thicken the trunc you need more foliage, for more foliage you need to let the plant grow. That means, a bigger pot/container, lots of sunlight. So as soon as temps are good enough, outside with it. Remove the pebbles, weed and moss.
G
For the repot some good quality potting/gardensoil and a plastic container will do, nothing bonsai ish needed as long as it grows