You sure want alot!!

How about a climbing ivy? Boston or English?

I doubt anything can meet all those requirements. How about artificial vines.

Hmm. How about kiwi vine (Actinidia kolomikta)? It needs male and female plants to fruit, so if you only have one you should be safe from fruiting. I've heard the flowers are inconspicuous, so I don't know if bees are an issue with it. It's vigorous and hardy to zone 4.

Alternatively you could start wisteria from seed in a big pot... I've heard it takes years to start flowering. If you hardprune it every year it should stay in bounds without tearing apart your pergola.

The Boston and English Ivy seemed too aggressive for our needs. The leaves are large, and we were afraid that it would completely carpet the pergola. Also, doesn't the ivy root bury itself into wood surfaces? We wouldn't want it destroying the cedar.

I will look in the kiwi vine and wisteria. One website indicated that the kiwi was only hardy to zone 7. Is that right?

Please do not plant anything. If you do plant something before you know it insects, especially precious 'honey bees', will swam around you and you will grab a can of poison and kill the 'honey bees'. If you are alergic to insect stings please do not create any outdoor activity. Stay indoors!!! DO NOT KILL OUR HONEY BEES or any beneficial insects!!
Most folks who are allergic to insect stings do not eat right. They load up on sugary foods, drink alcohol, drink soft drinks, smoke. Adjust your diet and don't kill out insects.

I just checked back with a suggestion I can't believe I forgot since it's growing right outside the window of this room, and I see you're actually a bee assassinating, beer swilling, cigarette puffing sugar junky :) lol But can I offer my suggestion anyway? :)

Winter jasmine. It's just the thing. An evergreen vine, vigorous and attractive, which flowers at a time when you (or at least your bees) are unlikely to be around the hot tub. There's no fruiting mess to contend with, it won't hurt your cedar, I know of no toxicity to bathers, and it's hardy to zone 6. I don't know what zone you're in... is it 6 or above?

Oops, sorry, it's not evergreen, where is my brain... but I think the rest of what I said is okay.

How about something that is a night bloomer? Moonflower opens in late evening to attract moths that pollinate it but I think the bees will be gone for the night by then.
It grows quickly and can be grown from seed. As far as I know it is not toxic and can be cut back at will.

Staying indoors is an absurd suggestion although I did get a laugh at the image painted of your wife as a bee swatting, poison spraying rambo while chugging beer and smoking up a storm.

Best of luck!

How about Dutchman's Pipevine (Aristolochia durior/macrophylla)? It has curious flowers that are not attractive to bees. It is a twiner and thus will not damage your cedar with rootlet attachments like ivy or Virginia Creeper. It is a native and host plant to the rare pipevine swallowtail butterfly. It is cold hardy in your area. As it is deciduous, you can prune when it is dormant to maintain size. This is the vine that was popular 100 years ago with rural folks for covering dining and sleeping arbors. Google it by inputting its botanical name and see if it suits.

That said, I am not sure you want a vine at all. Nature up close is always somewhat messy. A cedar trellis provides privacy, stays where you put it, doesn't shed, make you break out in a rash, and doesn't decompose. Most gardeners who love vines are attracted to the lush wild effects they create. This seems to be the opposite of your needs.

Virginia Creeper by the way is not toxic to anyone. Its leaves resemble poison ivy, but mature leaf clusters are in groups of 5. Poison ivy grows in leaf groups of 3, like a trefoil. Children are taught, "Leaves of three, let it be." Virginia Creeper is the "ivy" that covers the Ivy League Universities. Whether they deserve it or not, those college kids can't be trusted with wall after wall of poisonous vines they must not touch.