Blade Dancer

This is entirely broken. Human, first level fighter, fourth level rogue. Great sword, this feat. Max dexterity, everything else doesn’t matter. Get advantage on an attack. -5 on attack roll for 4d6+14 damage. Then, when you split the first guy in half, you get a free attack during the attack action and as a bonus action.

It sounds cool, yet it is OP. I would say the bladed weapon must be a finesse weapon to qualify, not made a finesse weapon. The last ability should be dropped or nerfed so the follow up attack is at disadvantage and must be within 5 feet(hey, you are getting the opportunity to use your charisma (performance) modifier for attack rolls which has some cool flavor)

It is OP, and I will tweak it, but I LOVE the idea of it.

I don't think you read how this works at all... you cannot get the bounce on your damage roll. you use it on the attack roll

Even so, it is to strong. In most cases people want to tweak this down. Two handed finesse? Thats crazy, and easily abused.

I'm assuming the author only meant for the advantage on Performance check just for checks and not weapon attacks using Performance but I can see how that is easily confused by the way it was written. I think there is an easy fix for this feat to make it "balanced" just be rewording and changing a few things.

Choose one bladed melee weapon type you are proficient. When wielding this weapon you gain the following benefits:

• You may use your charisma (performance) modifier in Charisma modifier when rolling attacks (but not damage) with this weapon.
• If the weapon is not already it counts a finesse weapon when you wield it. If the bladed weapon you chose is a one-hand weapon, it will gain the finesse property.
• You have advantage on any performance and intimidation checks made using the weapon.
• Whenever you score roll a critical hit against or kill an enemy you may make an additional weapon attack as part of that action. ,you can make one melee weapon attack as a bonus action with that weapon.

Check: 
"When wielding your weapon of choice, you are so fluid and graceful ..."
"Choose one bladed, melee weapon type you are proficient with."
"You may use your charisma (performance) modifier in when rolling attacks (but not damage) with this weapon."
"If the weapon is not already, it counts as a finesse weapon when you wield it."
"You have advantage on any performance and or intimidation checks made using the weapon."
"Whenever you kill or score roll a critical hit against or kill an enemy, you may make an additional weapon attack as part of that action."

I'm sorry to nitpick, especially with the last line, but readability, wording and proper grammar are one of the cornerstones of the game. 
All of that said, I like this feat but I think there are some pretty apparent balance issue that come along with it at the moment.
I think the suggested changes from Vorkyvorky are certainly worth considering.

one of my players accidentally put this on their sheet and they asked me about how it got there, we spent the next 30 minutes trying to find out where the hell they got it from, and it turns out they never even used it and simply had this broken feat in their sheet. I really love the idea of a Bard/Rogue hybrid critical striking on an unsuspecting enemy with a stealth attack, but sadly it is too OP

put this on a rogue, take like a halbard or any other polearm, sentinel, polearm master, and have expertise in performance and you literally are just unstoppable.

This is so incredibly broken.

Imagine running this on a hexblade pact of the blade warlock with great weapon master. You get extra attack with your pact weapon, +1 on hit and damage from improved pact weapon and if you land a crit you get to roll for another free attack and then you can use your bonus action to make another attack that could potentially proc this feat again.

Remove finesse thing change extra attacks to free weak cast of charm person or just intimidatetion