There is a birth defect called "bent neck" that you could look up. It's just something that happens occasionally. But you question sounds like all the flowers are like that. Do you have a picture?

I think any kind of anomaly that happens during the early stages of bud formation may cause this. It could be a genetic mutation, the weather conditions, some kind of insect infestation or a result of a chemical spray at the time when the buds are just beginning to form on the new growth. They're probably not even visible as buds yet. Sometimes the bloom will open and be perfectly normal but sideways. Other times the bud will produce a malformed bloom. I usually let them bloom to see what they look like out of curiosity. If you have a lot of them think back and see if you can figure out what was going on between 4 and 6 weeks ago that may have caused it.

I have never seen more than one bent neck at a time. The material cause is a ribbonlike thickening on one side of the stem that makes that side stiffer than the normally round side.

I've never seen more than one on a bush either, Michael. I have seen several through out the garden at once though.

If you have a lot of them happening on a bush, dmoore, then we need to see some pictures.

Which roses (or is it all)?

My only addition is to check the neck. If there are brown or black marks, it could possibly be midge. Midge damage can either be the "crispy burned" tips or damage on the neck.