As everyone else is saying, wear a mask if you have one.

But it seems like the question you’re directly asking is more about the fluid flow of air in the room. With your suggestion of alternating short/long breaths, you might be imagining that you can blow the germs away and then breathe in the clear space left behind, but of course it doesn’t work that way. Blowing or breathing quickly creates more turbulence, which stirs up the air and sucks in more air from further away—both of which increase your risk. (Reducing turbulence from your breath is the second function of a mask, besides filtering out particles.) In the best-case scenario, the germs are in large aerosolized droplets which will settle out of the air quickly, but only if the air is still—so you’d want to breathe softly and move as little as possible. (And the droplets can still be infectious after they fall, so wash your hands after touching anything as well.)

Here’s a very technical paper that studied nose vs mouth vs combined nose-and-mouth breathing:

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7455204/

I confess it was over my head and I just skimmed it. But the conclusion says, “The high filtration efficiency of the nasal cavity together with its efficient clearance mechanisms lead to the recommendation to prefer the nose breathing over combined or mouth breathing.”

The conclusion also says, “There is general scientific agreement that lower airways are more vulnerable to severe infections” and “From this point of view, the nasal inhalation is preferential because it significantly reduces the number of particles penetrating to lower airways.” I’d guess that means that shallow breaths are probably preferable, but you’d need to read the article to confirm that.