It just means "no problem". People add "bob" because it rhymes with prob. Earliest usage can be found in the sit-com "Family Matters".
by Shoken April 18, 2016
Zit 1: "hey Eric can you help me with your magic sword +1? we must defeat the black dragon!"
Zit 2 : "No prob Bob!
Zit 2 : "No prob Bob!
by heythewhat January 08, 2012