Canon? non-canon?

My Bardock follows the original story, implying the first TV Special and the OVA 'Episode of Bardock'. He's not an AU character, nor a "what-if" character.
Though, I did develop him quite a bit, starting with his personality.
I made the choice of mixing his personality from the TV Special Bardock and Minus Bardock, plus adding some extra details.

personality changes: his family

In my version, Bardock has different feelings towards the members of his family: he almost despises Kakarot (aka Goku) for what he did once he landed on Earth (protecting this planet and befriending its inhabitants). He's proud of his strength, but not of his motives. At all.

On the contrary, Raditz does earn some points in this subject, because of his Saiyan personality, thus making the father more proud of his first son.

Finally, I decided to keep his love for Gine unchanged. She's the one who taught him love, and he'll do anything to keep that feeling mutual between them.

personality changes: other characters

For the most part, this version of Bardock doesn't have any particular changes of personality with other Saiyans. They may be some exceptions here and there due to SLs (for example the one with Cress).
Though, his relation with Vegeta is something else. Just like he despises Kakarot, Vegeta gets the same treatment. To him, the Prince of all Saiyans isn't allowed to be one anymore, since his behavior and personality have totally differed from before, and not in a good way.

Finally, he /hates/ fusions. According to him, two beings fusing to create one with increased power is a cowardly way to get stronger, since it just shows that they couldn't get more power by themselves, making it ridiculous and shameful.

Super saiyan

From the OVA 'Episode of Bardock'

Super saiyan 2

Obtained via a solo: https://twitter.com/LowClassLegend/status/578268289656352768

Super saiyan 3

Not from a solo lol, I just decided that he'll have this since Xenoverse 2 introduced Bardock in this form.

Super saiyan 4

Obtained via a solo: http://www.twitlonger.com/show/n_1sol3c8

evil bardock /masked saiyan

Officially introduced in Dragon Ball Online and then reused in Xenoverse 2. I didn't do any solo since this 'form' already was introduced in both those games. This is not really a transformation, it's more of a mind control with a massive power increase.
The only time I'll use it is in SLs or themed events like Halloween for example, because I want some story and explanation before the 'transformation' occurs.