bonnie wrote:

Given, CFL's are thought to be more energy efficient than incandescent
bulbs. But I heard they use more energy to turn on.

The turn-on energy difference is miniscule, but each start removes about
6 minutes (0.1 hours) from a CF's typical 6000 hour lifetime at a typical
$2 cost, vs a bulb's typical 750 hour lifetime at a typical 50 cent cost.

What if it is in a room that is used infrequently, a closet or guest
room for instance. In other words a room in which you would go in and
out of pretty quickly.

How long would a CFL have to be left on to realize the net energy savings.

You might better ask "How long would the CFL have to be left on per start
to save money over an incandescent bulb, with 1/4 the power consumption,
at 10 cents/kWh?"

Nick