OK, it's only a try
The speaker is (or is related to) the ABBA pop group
I needn't be late, that would be bad As a man with a job, I must get to work
SOS song by ABBA (of course, a SOS signal must be responded very quickly, otherwise it can turn bad).
I must travel quickly now, so I go I travel by the underground train
Waterloo by ABBA (it's a London Underground station).
I have bills that I need to pay I need that money to live
Money, Money, Money by ABBA (probably no explanation needed).
My name is just a name, it's rather dull If you feel lonely, as I do, feel free to give me a call
Take a Chance on Me by ABBA; and the name of the group is... well, rather dull, since it's a mere abbreviation.
music tags not only show that one need some knowledge in music to answer the question, bus also probably reference Knowing Me, Knowing You and Thank You For The Music songs, also performed by ABBA.