Those bulbs are pretty well water proof - they have to be - they're gas-filled.
The starters and chokes are not water proof at all - and if your bulb is "smoking" it's more likely to be a problem with the choke etc
Disconnect - dry thoroughly - (like take apart, dry off what you can, and leave for at least 24 hrs before re-assembling) - and you "might" be ok.
Continue to use it as it is and you risk blowing the whole set-up (and starting a fire thread)