You definitely want one rated for outdoors. Most of the modern motion bulbs are LEDs and you'll not really have to worry too much about what the bulb form factor is. It's not going to heat up enough to matter.

The Sengled SS-PAR38NAE26W LED with Motion Sensor (Smartsense), PAR38 is an example of a motion-sensor LED lightbulb. I'd recommend that the bulb you choose be no brighter than 1000 lumens (equivalent to a 75 watt incandescent bulb) with a color temperature no higher than 3000K.

You might want to consider switching to a "Dark Sky" compliant fixture. This website discusses light pollution and here are some Dark Sky fixtures at build.com. Note that these fixtures focus the light downward where it is needed rather than into the sky and surrounding environment where it is not needed...or wanted.

Thank you all for the information. I didn’t realize that the fixtures were not that expensive. I think I will go ahead and have one installed. My flood light is 17 years old and probably needs replaced anyway.

We have installed the motion sensor light bulbs for outdoor use and they work quite well. The issue is the same for both fixtures and bulbs only...keeping people from flipping the switch and accidently turning off the light.

I know I'm coming into this a little late but I would strongly suggest buying a fixture that uses actual bulbs rather than having the LED built in. Sooner or (hopefully) later the LED is going to fail, with built in LEDs the entire fixture goes in the trash. If the bulb fails, just replace it. Same goes for the motion sensor. You can actually buy a replacement motion sensor but for $5 more you get the entire fixture. Just put the old bulbs in the new fixture.