does bardic inspiration help the individual?

Yes and no, I suppose.

No in the sense that, if you're looking to consistently dps down generators by yourself, using Bardic Inspiration is almost always a net loss on progress relative to if you did not use the perk and just did the gen solo anyway. For reference, you'll need to hit 17/9/6 skill checks solo per Bardic cast just to break even with the cost of casting it in the first place for 1/2/3 bonus progression rolls. You can increase the chance of you hitting these thresholds with perks like Deadline, Hyperfocus, Toolbox, or a combination of all of them.

That said, the perk has two benefits outside of its straight solo use that provide value:

1. Using Bardic in a safe place, then bursting down a generator
2. Using Bardic with at least one other person around you

#1 has the benefit of you being exposed on a generator for a shorter period of time since it will finish faster with the buff on than without it. The time wasted is still likely to be higher overall, but there is some value in being around the gen itself less. The downside here is that by the time you cast the buff, you might need to help your time and therefore waste that time entirely.

#2 is only a benefit if you are FORCED to do a generator as a group from start to finish, since doing a solo gen is always going to be more efficient. Even though you take 15 to cast the perk, the other survivor will be working on it without a repair penalty (which you get from multiple survivors on generator), reducing the actual time you waste casting it to about 6 seconds worth of gen repair time. That means the threshold to break even with the perk is now 6/3/2 skill checks on +1/2/3 bonus progression rolls.

Keep in mind, although 6 skill checks seems duoable on a duo generator, in my experience its not uncommon to get ~5-8 skill checks in the time it takes to duo one generator. That means the chance of getting a practical benefit from the perk is possible, albeit low, and the benefit itself is usually not worth the risk. If you can 2 generators as a group though, you'll start seeing some value - probably ~10-20 seconds saved in total for both gens if I had to guess?

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Overall, think of this perk as a waste of time to use unless you need to burst out of a 3-gen hold or some other high traffic generator that you don't want to sit on for too long.

You can also improve its value by running things like Deadline, Hyperfocus, Toolboxes, etc. The exact amount of value you'll get through the inclusion of these perks is variable though.

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Edit:
I've said this elsewhere, but I REALLY hope the developers buff this by making the perk have a dynamic cast time based on how well you roll. i.e. a roll of 0 cancels the performance; rolling 2-10 takes 5 seconds; rolling 11-19 takes 10 seconds; rolling 20 takes the full 15 seconds.

Or at least make the cast time required to keep the buff dynamic, and the actual play time can stay at 15 regardless (if you want to play for memes)

That way you can use the perk more consistently and efficiently without changing many numbers. It also feels terrible to roll between 1-10, realize you will get no value from the perk, and have to cancel the performance because it's not worth it. That happens in literally 50% of cases, which I think is really disappointing.

No worries!

And I wish - even that would be better than what we have.

The cast time is a static 15 seconds, and you have to stand still for the entire 15 seconds or else you will not get the buff for 90 seconds. Instead, it will just fall off as soon as you finish playing if you cancel it early.

Also keep in mind that the buff is centered around you, and a 16m range around you. This means that if anyone leaves that range, the buff falls off on them; however the reverse is true, where if they get back into that range, they will receive the buff again.