Those are fine -- leave them be, and just get the plants planted, NOW.

When you plant them heal up the canes with soil or mulch so the canes won't dry out!

Just to report a follow-up.

I did cover the bush with soil and mulch and we had a cold snap for 2 weeks after I put them in the ground. So that slowed growth down and gave them more time to root.

Nevertheless...
It turns out that although the bushes as a whole survived, the branches produced by those buds were weak, never bloomed, and eventually died. Subsequently, the cane died back to below those buds.

So I'm going to confirm other advice online and say NEVER buy any bare-root rose with any bud growth at all.

I think it's the wax on the canes, not the tiny buds you see there that caused the problem. The cheaper growers wax canes so that they stay green on store shelves. I've never had a waxed cane do well even where I am (and in Coastal Cal I'm in a much cooler zone than Arizona). The buds were fine -- leave them on.

But ditch the waxed cane bareroots, unless you can imagine the plant without those particular waxed canes and still see a decent plant worth buying. Some bareroots are waxed only at the tops, and those ones are usually ok, because the bottom of the cane is all you need. And by the way, I've tried everything from fingernails to credit cards to hiar driers to get that wax off before hot weather burns the cambium layer of the canes -- nothing seems to help those canes to survive. They all die anyway.