No, there are no such thing as plastic inner pots for bonsai. Bonsai is kept in a ceramic pot with lots of drainage.
If you are worried about drips from the pot you are proboably keeping your tree indoors, which is the most common beginner misstake. Trees should be outdoors most of the year. Some species needs protection during the coldest part of the year, but that is at lover temperature and not much watering is needed.
Topfrog is right. I have a few tropicals, and they come inside when temps are <50F/10C. Sometimes I take them back out if it will be warm for a while, but that is a big production since some of them are pretty heavy. When they come inside, all three lose leaves. The baobab drops them all and tries to grow some more but doesn't do well until March when it goes back out side. The ficus drops leaves steadily all winter, and the jaboticaba drops a lot and new leaves slow way down, only starting to grow leaves again when it goes outside. They sit in a bay window with a lot of sunlight. I have been thinking about getting lights for them to compensate for the sunlight.
Lucr puts it shorter: trees belong outside.