"I'm busy" is just a polite way of saying stop talking to me. I should know, I've used it myself.
Nobody is ever too busy to not at least send a quick text once a day or something, don't fall for it.
Mehh this is why I prefer if a person would be polite but upfront.. like just say like "please stop talking" .."Im busy" is like a poor excuse even though most of the cases they arent...