You seem to not understand the concept of "random variable". The term "random variable" does not refer to a variable that is unknown, it refers to a variable that has a nondeterministic relationship with other variables. For instance, when you draw cards in poker, the result is a random variable. Just because you end up knowing that you ended up getting particular cards doesn't make them not random variables. You can still ask what the probability of getting those cards is. And since your opponents' actions will be based on that probability, you'd better be able to figure out what that probability is. If you're thinking "Well, I know that I have a pair of kings, so clearly the probability of having a pair of kings is 100%", you're probably not going to do well. To do Bayesian reasoning, you need to know what your prior probability of getting a pair of kings is.
For a more complicated example, suppose you have a population with mean $\mu$ and standard deviation $\sigma$. You then take a sample and calculate the sample mean. You then want to calculate the 95% confidence interval. This is an interval such that there is a 95% chance that your sampling procedure will result in a sample mean within the interval. This is often presented as "I have this sample mean, and there's a 95% chance that the true mean is within this measurement error". But this is suggesting that the true mean is some random variable with some probability distribution. But it's not a random variable, it's a fixed parameter. It's the sample mean that is the random variable, and it's the sample mean that has a probability distribution. Just because you've already taken a sample, and know what its sample mean is, does not mean it's not a random variable. There is a nondeterministic process that turns a population mean and std into a sample mean. The sample mean depends on the population mean, but does so nondeterministically, and so is a random variable. Similarly, you valuation is being modeled as coming from particular parameters, but doing so nondeterministically.
Presumably, your bid will be based on how much value you think the good will generate for you. This will in turn be based on what information you have received about the good. And what information you receive can be modeled as a random process. Basically, you have a good space G. You have some data space D. You have some valuation function V. Given a particular g in G, there is some distribution of D: p(D=d|G=g). Given a particular d, there is some valuation v: v = V(d). You want a strategy, given v, of choosing a bid. v is a function of d, which is a nondeterminstic function of g, thus v is a random variable depending on g. Given a particular v and a prior on the distribution of G, and the conditional distributions of d on g, you can use Bayesian reasoning to find the distribution of g. You can then find the bid that maximizes expected value (i.e. the value for each g, weighted by their conditional probabilities).
As for why the bid shouldn't just be your valuation: there's no reason to think that your valuation will be an unbiased estimator of the good's true value. Furthermore, the expected value of a bid has a complicated relationship between the bid and the good's true value. If you win the auction, then the value of your bid is the difference between the value and the bid, but the probability of winning the auction depends on your bid and the other participants'. Thus, even if you did have an unbiased estimator of the true value, you shouldn't use it as your bid; you need to take other participants' bids into account.