Whereas a frequentist model looks at an absolute basis for
  chances, something like the population of females is 52%, so that
  means that if I select someone at random from my office, I have a
  52% chance of picking a female. The chances are purely based on
  the total probability. The Bayesian approach is to rely on past
  knowledge and then adjust accordingly. If I know that 75% of my
  office is male, and I grab a person, then I know that I have a
  25% chance of picking a female.

This is a terrible example, it makes it look like frequentist statistics don't know about conditional probabilities.

My understanding is that frequentist statistics are all about point estimates (such as maximum likelihood) or sometimes confidence intervals. Say you want to run an elections poll, sample a bunch of people and ask who they have voted for.

Frequentists will average the data and say "Party A is at 51%" (point estimate) or "Party A is between 49% and 52%" (confidence interval). Asymptotically and under certain assumptions this value will converge to the "real" value and often you can also estimate the speed of convergence (with variance bounds).

Bayesians will instead start with a "prior" which is a probability distribution p(x) on "Party A is at x%". You can start from an uniform, non-informative prior, or if you have some information you can factor it into the prior. Then you take your polls data D and compute the conditional probability p(x | D), called "posterior", which is the probability that "Party A is at x% given the data". So you don't get a number or an uniform interval, you get a probability for each possible electoral outcome. Again, if you have infinite data this will converge to a distribution where all the mass is on a single point, which usually is the same given by frequentist statistics.

The problem with Bayesian statistics is that you have to handle probability distributions instead of single numbers (as with point estimates), so the inference gets extremely harder. It has been made somewhat possible only recently thanks to both algorithmic and hardware advances. On the other hand, the main advantage is that you get to know how uncertain your estimate is, which can make a huge difference when you have little data.

Last note: another thing you can do when you have a prior is factor it into your estimator and take the maximum likelihood of the posterior as a point estimate. This is called Maximum a Posteriori (MAP) and called by some people "Bayesian", but I don't think Bayesians agree with that.