bartonella is described as microaerophilic - ie it likes a small amount of oxygen for optimum growth
a quick google on conditions used to grow it in culture turns up this
paper said...
For optimal growth, pH of the medium should be 7.0–7.5.
Most bartonellae are both microaerophilic (only a small amount of oxygen is required for growth) and capnophilic (growth is enhanced in the presence of increased CO2 in the atmosphere)
https://www.sciencedirect.com/topics/agricultural-and-biological-sciences/bartonella#:most species of bacteria that are microaerophilic do not like large quantities of oxygen - so i would say the chances are it will not somehow supercharge bartonella growth - as otherwise they would be using higher concentrations to culture it in the lab
that is not quite the same thing as saying that oxygen therapies will kill it - i am not sure if we have any scientific evidence for that
bartonella lives in red blood cells - and red blood cells are designed to carry oxygen around the body in side them also - so bartonella seems to have evolved to deal with reasonably high concentrations of it.
its also been found to survive in things like rodent, flea and louse faeces for long periods - even when exposed to the air - so it seems quite robust in that regard.
all that said - that's all in line with the idea that the oxygen itself is having a direct deleterious effect on the microbes - but i am not sure if we know how oxygen therapies like HBOT actually work ( or perhaps even - if they work?) - ie are they having an oxidising effect that is in itself antimicrobial - or are they modifying the immune system in some way that helps the host fight the infection - i am not sure if its been discovered
i hope its of some help