Unless they were allergic or a ton of the bees stung them, the bee stings would be no more than a mere annoyance to them. But they're fine in the next scene, which suggests to me that they either did not get stung or not many bees stung them.
I've got stung by a bee a few times growing up, so I know how painful it is. But a bee sting is not usually serious. It's usually very minor and requires little treatment.
Being stung by bees is not the worst thing that happened to Ducky and Spike. As I said before, they had to face lava in the first movie, and there's no way getting chased by a horde of bees is more traumatic than almost falling into lava.
And the gang has been through things that I would consider worse than a few stings. Here's a couple of them:
-When Cera was getting chased by the crazy domeheads and almost gets crushed by them
-When Littlefoot almost because lunch because he stood inside a sharptooth's mouth
-When Cera and the twins fell from Saurus Rock
-When Cera twisted her ankle (yes I consider this worse than bee stings because it hinders her walking ability)
-When Petrie's wings froze in the sky and he fell down
-When Littlefoot was almost killed by Ozzy and Strut
All these things I would consider as worse than bee stings. Bee stings, while painful, are very minor, unless you're allergic or a lot of them sting, neither of which was true in LBT6 since Spike and Ducky are not on the ground moaning from the stings, or getting treated for it.