If you make a bid lower than any of the existing sell orders, then the bid will just sit there until someone acts on it and sells to you at that price, which could be 1 second from now or forever.
Hidden orders do not affect the bid price. The "bid price" is simply the highest price being currently offered publicly for the good.
If there is some secret buy order higher than bid price, then the bid price does not change.
Note that there should be no "hidden" orders in an honest exchange, because if such orders existed then it would cause anomalies such as phantom executions. For example, let's say that that there are 3 orders: a buy order for 100 at 20, a sell order for 200 at 22 and a secret buy order for 50 at 21. Now, someone enters a market order to sell 100. Then, what will happen is that 50 will be executed at 21 and and 50 will be executed at 20. This will be confusing to the market participants because the question will arise, where was the bid at 21? If the answer is: it was secret, that will piss everybody off. As far the major exchanges are concerned, there are no "secret" orders for that reason.