Applying for a PhD after taking a year off I completed my Master's in biotechnology exactly a year ago, and after failing to find a job in science took an office job to pay the bills. Now I'm thinking of applying to a bio PhD, but I'm worried my year away from science will be a disadvantage to me on an application.

How much will this affect my chances, and is there anything I can do to counteract it?
I am in an academic field -- mathematics -- which must have one of the highest rates of "going straight through" of any academic field.  E.g. in mathematics it is quite common to get your PhD before the age of 30, which makes it almost impossible to spend significant time off.

The most important word in the above paragraph is significant.  Taking one year off between degree programs does not -- even in mathematics -- generate a blip on most admissions people's radar.  What that means is that you waited to finish the program you were in before applying to the next one: that's really quite reasonable.  

I would mention how you spent your year off in your application materials precisely if it paints the rest of your application in a positive light.  E.g. if the job you took is relevant to the program you're applying for, go ahead and mention it.  If you just took that small amount of time to find yourself and generate sufficient resolve to attend a graduate program: no problem, but unless that fits perfectly into some narrative you'd like to spin I wouldn't dwell on it much in your application.

TL;DR: This is really not a problem.