I would probably just pressure wash it as best as you can....maybe "unwind" the vine some and then loop it back...otherwise....the bleach may burn or kill it.....if you go that route....water the vines down first and thoroughly rinse the vines off as you go. I think Jomax is plant friendly...it's a pre-packaged cleaner you can put on the end of your hose.
Bleach is not the best for wood cleaning as it alters the pH quite a bit. I have been using the cleaning and brightening products from Penofin for years, they are more of the oxygen type cleaning type.
What type of vine do you have, Bill? If it is dormant now, I would be less concerned about the affects of the cleaner.