They have very similar meanings. The first one "I'm going to take a bus to visit my friend" makes it sound like you are in the process/action of going right now.
"I'll take a bus to visit my friend" tells someone what you plan on doing, but you are not necessarily doing it right now. The first sentence could also be said without doing it right now, but if you were leaving to take a bus right now, you probably wouldn't use the second sentence.
Hope that helps!