It's really hard to say what I would do. If she was ready on three events then it would generally seem appropriate to me to give her the summer to train L6 and evaluate where she is after that. As well, I think she should be aware of the concrete things she needs to achieve on bars in order to compete L6 (i.e. these skills to this degree, correcting these problems) and exercises she can work on in order to gain strength and flexibility.
My highest L5 bar score was an 8.0 and I'm pretty sure I got through my entire level 6 season without ever even getting an 8 on bars...my L6 bars were interesting to say the least, it would probably take a lot of time to go into all the specific problems.

Did not repeat L5 or L6 as I showed enough improvement on bars (clean cast HS, free hip HS, giant - although I ended up competing free hip HS flyaway that year because the giant wasn't that great - and a good layout flyway). I got a 9 something on bars at L7 state and third place. The next year in L8 I averaged a 9.3 and scored as high as 9.65 (1st place) at L8 state. So I'm not that down on it but my problems were admittedly a little more unusual maybe than the ones most people struggle with on bars. Since I went to kind of a rec gym until I was a L6, I never officially learned a tap swing until I moved to L7, and my wonderful, beloved 7 and 8 coach taught me everything in a relatively short time period

Those other two years we had kind of shuffled through a few coaches and I think they all figured I'd been taught a tap swing and was just unfortunate, I don't know. Most of my group who had always been on a team track had good bar basics, so I think I just looked like someone who wasn't catching on or something, lol.
My other events were pretty advanced for a L5 because the coaching at the rec gym was good, we just lacked bars equipment and did not work on it a lot. I also struggled with the connections because I hadn't really ever worked on connecting kip-cast exactly, since we didn't really work on routines like that. I got moved up probably basically because I was already a L6 on everything but bars in L4 since I had just been learning skills the years before and had BWO on beam, had worked BHSs, had BT, FT, and aerials on floor. I was older because I hadn't come through a pre team track and very driven to move up. I guess it would come down to a lot of things, like age, the specific problems (lack of strength vs lack of basic technique), how the gymnast feels about it/personality (perhaps because of the weakness, moving up would be a lot of pressure and the gymnast would rather address the weakness at L5 where she will also see success on other events), like any move up there are very individual circumstances that need to be addressed.