I am certain there is a really simple way of doing this and I am just too
stupid to figure it out...

I just want to have Row 1 Column B show a start time I manually enter (say
9:15PM), then be able to enter 10 (ten minutes) in row 2 column A to show a
value of 9:25PM in row 2 column B.

Row 2 Column B has time value (9:20PM)
Row 2 Column A has minutes allowed (20)

In other words, add B2 and A3 and show them as a new time in B3.

Any takers???