It's my understanding that UV light (sunlight) is what possibly causes the yellowing of the bubbles, so....I definitely wouldn't recommend putting it in the sun.
(Not to mention you would fade the pony inside the bubble as well.)
Although...people have told me they had MOC ponies in dark storage for many years and they still end up being yellowed, so I don't think we have a definite answer on what causes some bubbles to yellow and not others. It's just something that happens during the aging of the plastic and I seriously doubt there is a way to reverse it.