How did Bardock travel back in time

The Super Saiyan legend

There are two things to keep in mind. 1.) Where did Bardock go (or more when) and 2.) The canonicity of the films.

Where did Bardock or more go when:

When Freezer hit Bardock with his attack, he was transported back in time in a thousand years. And single-handedly, a member of the freezing species disposes of it by becoming Super Saiyan. However, Chilled survived the encounter long enough to issue a warning about a Super Saiyan.

So there is no real inconsistency when we take this into account. The Saiyan myth has it that a Super Saiyan appeared 1000 years ago and Freezer fears this LEGEND. Bardock was a Super Saiyan 1000 years ago and let the fear of a Super Saiyan grow cold.

So overall: No inconsistency apart from the flashback in the series in which the Super Saiyan is portrayed as someone in a more ape-like form than a normal humanoid.

Canonicality:

The films are almost never considered part of the main canon and are therefore often ignored in the series. For example the Broly films ... no information from them ever appears in any of the series other than that Super is now using a broly-like transformation for a Universe 6 Saiyan.

There are exceptions, of course, like 2 films being incorporated (and remade) into Dragonball Super, but before that, the events inside the main series were largely ignored (and often raised a few skill questions ... if not ignored would be).