Say I own an in-the-money call option that I want to sell for profit. I learned that higher volatility leads to an increase in the "price" of a call option in order to compensate for uncertainty, but is this the bid or ask price? Per my example, I would think that higher volatility would make a market-maker buying price (the bid) decrease and the selling price (the ask) increase for the option (ie. the bid-ask spread increases for the market-maker in order to compensate for volatility). Does that imply that the more volatile the underlying stock becomes, the less in value my call option becomes because I would then be selling the option for less (since I'm selling to the bid, or the market-maker's buying price)?
While it's likely that higher volatility in the stock is likely to result in an increase in option prices, it's not necessarily so.
The primary driver in this is that demand for options results in higher price. Higher option premium means higher implied volatility which is calculated by iteration. Iteration is the reverse engineering of an option pricing model where all known variables (stock price, strike price, time remaining until expiration, carry cost and dividend if any) are plugged into the formula. The volatility variable is incrementally increased until it matches the option's price. That is the implied volatility. It's the volatility that price is implying.
IOW, demand drives option price up which in turn translates into higher implied volatility. The market is determining what your option is worth not the option's implied volatility or the volatility of the stock.
The bid and ask price of a security are determined by the market. If the security is illiquid, there are fewer participants and the market maker sets whatever B/A spread that he likes, subject to regulatory limits. Any trader can become the market on one side of the option by offering a higher bid or a lower ask price, narrowing the B/A spread. For stocks, you can be the market on both sides but not for options.