Phil can cross the bridge in 1 minute.
Karen can cross in 2 minutes.
Stinky can cross in 5 minutes.
Bubba can cross in 10 minutes.

First, Phil and Karen go across with the flashlight:

Phil (flashlight) >>
Karen >>
(2 minutes are now used up.)

Karen takes the flashlight back across to the others:

<< Karen (flashlight)
(4 minutes are now used up.)

Stinky and Bubba go across with the flashlight:

Stinky (flashlight) >>
Bubba >>
(14 minutes are now used up.)

Phil takes the flashlight back to the other side:

<< Phil (flashlight)
(15 minutes are now used up.)

Karen and Phil cross for the last time:

Phil (flashlight) >>
Karen >>
(17 minutes are now used up.)