Question: Can someone explain bid, ask, and the flow of common stock shares?

So, when I want to sell 100 shares of stock X, they are bought by the Market Makers and immediately sold to someone else? Or do the Market Makers have an inventory of shares (
do they ever hold onto the ones they buy).

Answer:

It depends on a ton of factors, but generally a market makers whole purpose is to provide liquidity so they buy with the intent to flip the stock right away and bridge the gap between bid and ask prices. On NASDAQ the market maker is required to maintain a bid and a sell price. So the answer really is it depends, but generally the immediately sell them as that's their purpose.