I'm not for sure and I hope someone that knows more comes along to check me, but I'm thinking your tree may be a serissa, which is a lovely choice for bonsai.
Serissa, like any tree benefits from being brought outdoors for spring and summer, once night time temps are consistently above 50. But it is a tropical and does need to come back in for fall and winter. While it is actively growing outdoors, it will need regular fertilizing. Any balanced general purpose liquid fertilizer, used half strength should be fine.
I can't see your soil due to the moss on top. Soil for bonsai should be mostly inorganic/ mineral/ gritty and very free draining. If your soil is dark and soft and peaty (like potting soil), it should be changed out when you bring the plant out for spring.
The top layer of soil needs to dry out between waterings. Best way to know when to water is to put a wooden chopstick an inch down in to the soil. Leave the chopstick there for a few minutes, then pull it out and look. If the chopstick is dark and damp don't water. If not, water. Water when it needs it, not on a schedule. When you do water, be sure you water thoroughly so that all the soil is moistened and water is running out the drain holes. Then let it drain and put it back, don't let it sit in water in the saucer.
While inside, it needs extra humidity, via humidity tray and misting.
It needs plenty of light. While in front of a window, it should be a south facing window. Otherwise you may need to supplement the light.