Market price does not need to be unique. Any price at which something is sold at the market is a market price by definition. For example, in the model of monopoly with perfect price discrimination every single consumer is charged different price at the same market according to the consumer's willingness to pay (see Mankiw Principles of Economics 5th ed pp 329). If two customers with different willingness to pay would come at the same time and be charged 2 different prices both would be market prices.
However, this being said, you should note that it is not necessarily appropriate to say local fruit market and some nice bakery can be still considered to be same market. There is not, necessarily, a single market for bread.
You can have market for regular bread and market for more luxury bread or bread with some nice shopping experience, and markets can be also distinguished by location. Markets can be defined more narrowly (e.g. even single cafeteria can be considered market of its own), or more broadly (e.g your whole city to be part of one market for bread). This being said there are no hard rules how narrowly or broadly you have to define a market, but I think the above is relevant caveat to keep in mind. Generally, you would define market for modelling/empirical application in a way that makes the most sense for model you are going to use or research question you are trying to answer.
Does the market price change each time a different one of those stores makes a sale?
If you have different firms competing at the same market let's say firm A and B, you would denote their prices as $p_A$ and $p_B$. The correct way to phrase it would be to say that market price $p_A$ is different from market price $p_B$. Market price can change over time but you would track separately changes to $p_A$ and $p_B$.