I suspect the results would be quite poor. Incandescent filaments increase their resistance when they get hotter, so driving them at constant RMS voltage means that the power will decrease as they heat up, which will give them a degree of stability. At constant current, though, the power will increase with increasing temperature.
(Of course, they’re quite hot and radiative cooling increases like T^4, so this isn’t necessarily a show stopper. But it’s probably not helpful.)
For constant current, you'd need to drive at least 9 watts so it would be more like 250mA if not higher.
A 1600 lumen LED module might take as much or more current than a 60w incandescent. If your constant current supply can output between 0 volts and input volts, and it's set for an LED like that, it would be able to power an incandescent bulb.