(My stupid ass made the plot reliant on Vegeta finding the Dragon balls right at this moment to wish for a regeneration ability. The problem here is that, at this time in the timeline, it would be impossible for Vegeta to use the DB because Mr.Popo used them before, to revive the Namekian. So, by design, the Db should be a solid rock for a year. Again, my lazy ass didn't find a way to solve this problem, so I'll just assume that they are either not used or Vegeta can just use them now. I'm really sorry for the inconsistent writing on this, I'll get better...probably…. I hope?)
A few days passed and Vegeta realized that at least a month had passed since he had reincarnated in this world. In these last few days, Vegeta has been training hard, alone and with Piccolo sometimes. After a few days, unfortunately for him, the namekian couldn't keep up with his evolution and was losing too fast. Even though Piccolo's power was growing every day, he could not keep up with Vegeta.
So, now Vegeta was focusing on training alone. His power was growing but he still did not find a good moment to become a Super Saiyan. He was confident that he could become one before Freeza arrived, but he still needed the right time.
Vegeta was also interacting a lot with the Brief family while he was waiting for the upgrade of the Gravity chamber. The interesting thing was that Bulma's mother was one of the people that he could freely interact with, besides Bulma. She was a good woman to talk to, although she was flirting like her daughter calling him ''cool guy'' ''handsome'' and ''Bulma's boyfriend''. On these occasions, Vegeta could see Bulma shooting some dagger eyes at her mother from time to time.
In one of these interactions, Bulma finally reached him with the things that he wanted. A new set of gear and clothing. They were the usual Saiyan standards but a lot more light with the usual blue color and some with black color. Bulma said that he should use some variety in his wardrobe, so she put a few sets of colors there.
And the most important item right now is the Dragon Radar. Now he will be able to locate the Dragon balls and ask for the wish for a regeneration ability.
"You gonna ask for immortality from the Dragon ball, right? Most people want that as a wish. Don't know the appeal of these kinds of wishes.''
Bulma was talking while Vegeta was checking the device. They talked a lot in the last few days and teased each other, though Bulma took most, if not all, of the losses. It was hard to handle him, she thought.
"No not gonna ask for that right now, immortality won't make me stronger''
Bulma:''Hmmm, you are a lot more level headed than I thought. And focused too.''Bulma was looking at him with those eyes. When she looks at him like that, he finds it a lot more funny to tease her a bit.
Vegeta looked at her and smirked, saying,"Hmph. You pay a lot of attention to me.If you want to go to bed with me, then just say it''
Bulma's face went red, again her reaction was that of a teenage girl in love. She couldn't deny that the idea passed into her head, albeit for only a moment, and she refused. When she breathed and calmed herself to answer, she saw that Vegeta was already off to do his things.
"... Ahhh wait you jerk!!, at least don't let a girl talk alone, jerk, inconsiderate, idiot!''
Vegeta just waved behind his back to her while saying,
"If you want to talk to me later, just come to my room, I'll be busy from now on''
Unbelievable, Bulma thought. The guy was really acting like she was some low-class earthling, and things were getting even worse because now she is becoming even more interested in him, like she was just gravitating around him without a way out.
She gave a big sigh and went back to her room.
Vegeta saw 7 blips on the radar and went fast to collect them. These dots are shown around the world, but for the current Vegeta, it was easy to gather them with his speed.
After collecting the last one, he put them together to summon Shenron. The balls started to shine in an orange-yellow hue, the sky started to darken and a big Chinese-like dragon shot out of them.
''I shall grant thy any wish...But only one''
"Give me a regenerative ability on par or better than the senzu beans from earth''
Vegeta really thought about asking for something like immortality if the same regenerative ability that Zamasu showed in the future came too. Since he didn't know if this Dragon was capable of granting something at that level to him, he opted for the next option.
Something at the level of senzu beans would be a great boost, while the namekina regenerative ability would come in hand. They spend ki to do that, but what if he gains an ability that not only regenerates his body but his ki too? That would help him on his path, something even better than what the androids had.
''Guaranteed, though due to my lack of power, this ability will not pass to your descendents'' With this the dragon vanishes and the balls spread through the earth one more time.
Vegeta could feel that now his body had a sort of trigger where he could activate this ability or not. He thought that if it was automatic it would be better, but for now it's enough. He can think of another thing when it comes the time to search for the super ones.
Happy with now being able to regenerate his wounds without Dende's help, Vegeta's total focus was on training his body to the limit. Now with this ability, his power was rising even faster, he would spent his body's energy all day to the brink of breaking and heal it again. His power now sits at 5 to 5.5 million.
Finally, after 1 week had passed since he wished for the ability, Bulma came to him saying that her father finished upgrading the chamber that he wanted. Vegeta thought that he finally could level up with consistency and reach a new level of power.