Crib bumper - yes or no?

swbarnes2's answer is the "correct" one because the AAP has lots of data they are basing their advice on. Having said that, I used a breathable mesh bumper with most of my 5 kids because of their tendency to get an arm or leg stuck which at best woke us up at night because they were stuck and at worst led to minor bruising. When I installed my bumper, I wove it through the bars and pulled it very tight so that there was no way an infant would be able to get fingers or anything between it and the bars. The bottom was below the level of the mattress so that nothing could go under it, either. The closest we ever got to having any problem with it was that one of our kids had a tendency to sleep with her face smashed up against the side of the crib. We removed it for her as a preventative measure. Other than that, no issues at all. Perhaps we just got lucky and were being irresponsible/uninformed. I can't help but wonder if all these suffocation incidents were not the result of the bumper simply being installed incorrectly.

Either way, as for them jumping out... if you have a jumper, they are gonna jump whether you have the bumper there or not. The bumper might make it a little easier, but at that age, they progress so quickly that (at least based on my limited experience) there won't be much of a time difference between their first escape with vs without a bumper. ...AND if they are old enough that jumping is starting to become a concern, they don't really need the bumper, anyway.

Bottom line: If she really is hurting herself, as you say, you will have to decide as the parent whether the risk of suffocation is enough to prevent these injuries.

I originally didn't want to write this as a separate answer because swbarnes2's answer is perfect. However, I did want to add this extra info.

Without a crib bumper the worst-case nightmare scenario, that is almost impossible is a broken arm or leg without a crib bumper (and I have never heard of that happening, it would be a freak accident). With a crib bumber the worst case scenario is suffocation and I hear about that all the time.

The only time a crib bumper is appropriate is when the child's head can fit through the rails of the crib because of a deformity of the child. Even then, it's better to stick with other forms of sleep like maybe a flat crib matress on the floor instead of in a crib. This example child would be a very odd exception and not the rule. To be clear if there is no deformity, and the childs head fits through the slats then it's time to go get a new crib.

For most everyone the answer is no, crib bumpers are not safe, and should be avoided. There is a very small population of children that may need a crib bumper due to circumstances, but even then other sleeping setups should be attempted first.

The AAP says never use crib bumpers:

Crib bumpers (or bumper pads) may seem as though they can help protect babies from drafts and bumps, but they should not be used in cribs. There is no evidence that bumper pads can prevent serious injuries, and they pose a risk of suffocation, strangulation, or entrapment. In addition, older babies can use them for climbing out of the crib.

Source: Choosing a Crib