How do I resolve this conflict (if at all)?

I’m leading a team doing work on a deadline. This is my first foray as a team leader. It’s in a field where I’ve been around for a while, but it’s not my formal training, and I’m working with people who are both more experienced and knowledgable. Most of them have worked with me before and know this is my first gig as a leader. I also have a “boss” who is mentoring me in this process, so I have help, but my “boss” and I tend to see things differently.

One member of the team who is relatively new to the group rather quickly revealed herself as a bossypants, and frequently tries to interject her own ideas and agenda. My boss recognized she’s a bossypants and intimated that I should not let Ms. Bossypants take the reins. Trouble is, I see inklings of value in Ms. Bossypants’ ideas—underneath her bossiness, she has some worthy ideas (or at least is making lots of effort). The problem is that her energy is too overbearing, her knowledge is a step or two ahead of mine, and I’m not experienced enough to know how to really deal her both in terms of the pros and cons she brings to the table. Mostly, my instructions are to not let her take the reins.

So, eventually this escalates to a day when I have an agenda scheduled which involves everyone in the group and in the middle of it, she wants to change it to her agenda. Her agenda is related to the project as a whole, and I can see that. I also see that underlying her bossiness are some unmet needs that would allow her to improve the quality of the work she is responsible for, etc. So after so much persistence from her and the clock running short, I acquiesce. But, I do it in such a way that really puts her on the spot to come up with answers (to illustrate that she needs to STFU already because time is ticking and her special time isn’t coming to any fruition).

So, the next day and the day after that she starts working “offline” with individual team members and together they work out improvements. The improvements definitely work and enhanced the overall project.

I don’t care to hold a grudge. I don’t care really about who was right, but I also don’t want to reinforce her bossiness with positive feedback (because it’s been shown that people with crappy behavior continue that behavior if they are rewarded). The way I see it, she had the right ideas, but couldn’t be heard both because of her bossiness and because of my inexperience and inability to integrate her particular style and talent into my agenda for the group. On the one hand, I can understand where she’s coming from, but on the other I hear multiple opinions that she’s noticeably bossy.

I would like to clear the air before the project ends, but again, I don’t want to be a schmuck for someone who also has some fault to admit to. I don’t think it would work for me to apologize for my own stuff and then say, “but you were bossy,” because I think one really needs to own up to one’s own behavior.

My place in this group is secure, by the way. I could just never apologize or whatever and she’d be the one to go if it came down to it. That’s not my goal for this interaction. Just a fact of the case.

Thoughts?