How can I keep bugs off my spider plants?

It sounds like your plants have scales and they can be difficult to get rid of. Here's a link that will help:

https://www.thespruce.com/how-to-get-rid-of-scale-insects-1402693

f you have have a just a couple drops of essential oil like lavender or peppermint in a spray bottle with water (a natural repellent), mist the plant down. Then set the spider plant outside for a couple of hours on a cool day so the bugs will crawl off and go away.

Or if it doesn't get that cold where you live, try bringing the plant outside and washing the bugs off with your hose.

Check into diatomaceous earth. It is safe and should get rid of them.

Mix 40 parts water to one part liquid soap and then spray on the plants. Spray every 10 days to catch the ones that freshly hatch. Eventually, they will disappear.

On the rare occasion that one of my plants gets bugs, the first thing I do is repot the plant in fresh soil. Remove the plant, make sure you wash the pot thoroughly if you are going to replace in same container. Then wash the plant by running under water in the sink or outside with the garden hose, including all the roots as many pests are in the soil itself. Once clean, repot and treat with one of the remediesas previously suggested.

My grandmother used to give them a "bath" with warm (slightly) soapy water in the kitchen sink every other week to keep them at bay.

Spider plants are pretty hardy, but there are a few insects that love to turn them into dinner. Aphids, mealybugs, whiteflies, and of course, spider mites can all pose problems for your houseplants. Rinsing the plants with water is an effective way to combat pests such as aphids and spider mites.

I use the brush attachment on my vacuum cleaner. It may take a few attempts, but I do finally get all after the eggs hatch. I empty the vacuum canister outside afterward so the insects can happy live in their natural environment as Mother Nature intended.