Analysis of the bartonella henselae genome suggests that it has enzymes associated with vitamin B6 synthesis. Borrelia does not.
https://www.genome.jp/dbget-bin/www_bget?bhe:bh03780I don't know of any research that has attempted to quantify B6 production by bartonella in vitro. Anecdotally, people with chronic bartonella infections have reported high B6 levels, but there are possibly other causes for this.