I wouldn't advise it this late in the season. Propagating hydrangeas from cuttings is most successful if done from non-blooming softwood (or 'green' wood - 1st season) growth taken in spring or early summer.

You can try - shame to let the prunings go to waste - but you may not be very successful. The hydrangeas/hydrangeas website says getting the cuttings to survive through the first winter without greenhouse conditions is tricky and they recommend starting in late spring.

I was afraid of that. Thats why I put them in the garbage can in the first place. Then I couldn,t bare the thought of just throwing them away and rescued them . I think I,ll go ahead and give them a try .I do have green house but its unheated thats why I was thinking of in the attic in front of the window. I was really unhappy to be cutting the BB back so hard but the branchs were really twisted and contorted from growing in the middle of a big crowded nursey green house. It went from three feet to a foot.

I usually root Hydrangea cuttings in Sept., so they will develop some roots before the first freeze. All are outdoors, in pots under evergreen shrubs.
Some propagators "tent" the pots with clear plastic bags. I've tried it both ways and found no advantage to using the bags for conserving moisture. You just need to pay attention, so that they don't dry out or become overwatered.
Be sure to use a well drained soiless mixture. I use a peat based potting mix (10%) and equal amounts of perlite & coarse (builders) sand.
You will need to check the drainage holes in the pots periodically to insure that they don't become clogged! I once lost about 15 rooted cuttings of a rare blue lacecap sport, when that happened over the winter and the roots decayed.
Your unheated GH should be fine. If an early freeze is forecasted, you could cover them with an old blanket, straw, leaves, conifer needles or any other insulating material, which should be removed on warm, sunny days.
Roots should begin forming within 6-8 weeks.
I leave them in the rooting medium overwinter and pot/plant the rooted cuttings in the spring, after new foliage appears.
I have successfully rooted hardwood cuttings, by layering them in raised beds, with well drained soil and covering them with a couple of inches of soil and 6-8 inches of leaves, pine needles or both. Once they develop new stems and foliage, detach them from the old stem and pot/plant them where desired.
I just purchased 3 new Hydrangeas and once home, I considered removing some of the new growth stems and rooting them.
But after doing a search for more information, I found that all are Patented or PPAF, which after close inspection, I found disclosed in very small print on the nursery tags, which I had overlooked! Bummer!

I went ahead and stuck them in . I,ll be kind of surprised if any make it but nothing to lose since the plant was getting cut back anyway. I just hope I get blooms off it next season . I left three buds on most of the branchs. I put the plant up against the house under the covered deck so hopefully it will get a little more root growth before it gets too cold. When the leaves fall off I,ll put the whole thing under the house for the winter. It was hard to pay extra monney for a bigger plant then wack it back so hard but I am hoping the extra size means it had a bigger root ball so will bound back next season even if I don,t get flowers the first year.

Blushing Bride is one of the Endless Summer group and is said to be remontant and bloom on old and new wood.
If all of the old wood flower buds have been removed, you should still have some blooms next season, although they may appear later in the summer.
During the Easter weekend deep freeze, a couple of years ago, one of my ES lost all of it's foliage and blooms above a level two feet from the ground. New growth began immediately and within a month-six weeks, you couldn't tell that anything had happened to it. I was really impressed!
To me, BB does not appear to be as vigorous as ES. I have two, both planted to receive several hours of morning sun, but have not developed as rapidly as the two ES. One of those is located on a NW street corner and receives afternoon sun from noon until sunset. After two years to become established, it now produces more than 150 flowers each year, on a 4 ft. tall x wide shrub and even during two years of severe and exceptional drought, only needed watering once or twice during the year, when there was no rainfall for more than a 30 day period.
Be sure to keep the soil moist for your plant during the winter. I would place in a sheltered location, but one that would allow access to rainfall. You might even sink the pot in the ground, to be sure the plant receives enough moisture and prevent the soil from freezing in the pot during subfreezing nights.

Madeyna, are you planning to grow your hydrangea in a pot long term or is there some other reason for not installing it in the ground? This is a perfect time for planting in PNW - your hydrangea will need less attention next summer if allowed to establish in the ground over winter, accomplished by Fall planting. Even if you are a Z7 microclimate rather than a true Z8, they really don't need winter protection.

Thats great news that BB will reboom . I didn,t see that on the tag. I am putting in a new bed for the hydrangeas . It is 200 feet of mostly semi shade.I have a tall wooden fence there that will protect them from our really high winds. If the ground ever dries up enough I am going to put in a few loads of manure and till the whole area before planting any of the hydgrangeas.