This came from an idea I had while discussing DBZ with my friend.
What If: Bardock, instead of fighting Frieza himself, actually fled to earth with Goku. This will follow him, and show just how different things would be if Bardock was still around (Note: Starting from Dragon Ball Z, since I haven't watched the original DB) (This is a short chapter, just to show off the premise)

(ALL DBZ CONTENT BELONGS TO FUNAMATION, TOEI ANIMATION, FUJI TV, AND AKIRA TORIYAMA!)
Spoilers for DBZ

Bardock slams his fist onto the bloody rocks, where his friend's corpses lay. "D..darn it" He stutters to himself "Everyone I care about...and the entire saiyan race for that matter...their all going to be destroyed by Frieza, and none of them realize it!" He stands up, having just gotten attacked by Dodoria. 'I have to warn them!"

Bardock walks away from the town, growling as he hears laughter behind him "Those idiots! They don't believe me!" He punches the ground in anger "Fine then... they can all die for all I care! Raditz is on some mission. That just leaves me and..." He looks shocked at his sudden realization "Kakarot! Crap, he's going to be launching for a mission soon, I have to be there with him! I have to protect him" He flies in the direction of the spacepods.

Bardock finds his son's spacepod "there! Okay" He goes to the computer and begins to type "I'll just change his destination, then follow him in my pod" He finishes just as some other saiyans rush in. They see Bardock enter a spacepod next to his son, both preparing to launch

"Bardock! What are you doing, are you insane!?" One of them yells

"Stand down!" Another yells. Bardock ignores them and closes the hatch, having both his and Kakarot's ships blast off. He sighs in relief as he looks out the window to see the smaller pod

"Kakarot...you will never be in danger...I promise" He says. Suddenly, he sees other pods launch after him "Darn it!" He gets a video call from on of them

"Bardock! Return the pods now, or we have no choice but to turn you in to Lord Frieza!"

"Just try it! And while you're at it, ask him why he's planning to destroy all of the saiyans!" He yells back.

"What are you talking abou-" Bardock hangs up and opens his pod, shooting a blue beam out at his pursuers, causing them to spread out to dodge. He continues to fire, before shooting an asteroid and blocking the path behind him in debris. He chuckles and closes his pod, before falling asleep.