Yucca isn't a palm (nor a cycad), it's more closely related to asparagus. Probably better to put this question to the Container Gardening or House Plants forums.

for anything BUT mites you can use systemic insecticide: usually applied to soil and watered in. but it takes about a week for the plant to absorb it. so it is usually recommended to spray with some insecticide at the same time, while it's working it's way in.

it won't help with mites though. it's not clear from your description what kind of bugs you saw.

mites are very tiny, like a speck of dust. 1/2 mm is a bit bigger then that. so systemic should work.

I would take a pic of it during the day the entire plant when it has dried off. they could be mites, white fly, I would also spray the plant when you know for sure what they are.