A bonus that is only open to people who can go over and above hours wise is not fair.
But that's not actually true in the OP's case. It's not that she can't get sufficient billable time down during her working hours, it's that not a high enough percentage is recoverable because the files are going over the agreed fees. She could achieve the bonus during her working hours by either (a) negotiating higher fee estimates, or (b) finding ways to do run each matter more efficiently so she can keep wishing the existing fee estimates (either to do her own work more quickly or delegate more to junior fee earners (assuming that even if it takes them slightly longer, it costs the clients overall less because the hourly rate is lower - obviously doesn't work for everything on a matter, but it does for some)).
Negotiating better fee estimates may not be possible if OP is doing all her work for one client and there's already a pre-negotiated fixed fee for almost anything, but then the trade off is she's getting a steady stream of work, with scope and fees already set (my big time drain when I was a Senior Associate was always around the business development and scope/fees agreement). If it's not that situation then she needs to work with the partner to use the fact the client thinks she's incredible to negotiate higher fee estimates. Not always possible, but this type of thing is part of starting to be a more senior lawyer. Openly, law firms are businesses and if the clients loving her doesn't lead to more money coming in over someone who actually bills more recoverable time, she's never going to be materially financially rewarded or progress*.
She will be doing some of the efficiency stuff already, but there is always scope to improve there.
It won't be achievable for everyone without working extra hours but it is achievable for top performers because the constant stream of work is there.
*Not saying this is the OP, but to explain to people who think you should get a bonus just because of client feedback... Take two senior associates charging the same hourly rate and paid the same. One does belt and braces with the client, showers them with love and will happily spend long phone calls explaining all of the details. The second does a good enough job, but not the same belt and braces approach - client satisfied but not fawning. Second lawyer records half the time the first does because having the client love you takes time. Both approaches are valid but if the first lawyer isn't actually able to recover the extra time spent, then the second is far more valuable to the firm. Ultimately having a client love you only matters (to a law firm) if that helps the firm in some way. If she wants to make more money OP needs to find a way to leverage it, or she needs to become more efficient which will realistically mean the client satisfaction dropping a bit.
OP this is actually where in-house might be a good move for you - it's generally the other way round. Assuming it's not taken to extremes, very happy internal clients is usually far more important in practice than how much actual lawyer work you do. Closing one deal where the client raves about you is better than closing two where the client thinks you're so-so, even if on both the legal outcome is the same.