From my understanding of it „mit” translates to the English “with” fairly well. While „bei” also translates to “with”, the two can have different connotations. The simplest way I can put it is „bei“ is mainly used when talking about people.

For example: „Mit“ can be used in the sentence “I eat meat with cheese” = „Ich esse Fleisch mit Käse.“ In this case it wouldn’t really sound right to use „bei

Now let’s use a funny example that I learned from my German professor... suppose you are sharing a bedroom with your brother for some reason and you want to tell this to someone you would want to say „ich schlafe bei meinem Bruder“ which would convey your meaning that you sleep in proximity to your brother. HOWEVER if you were to use „mit“ in this example, a German speaker might assume you are partaking in incest!

A native speaker would probably explain the distinction better though.