There are specific amendments in the Constitution that are driven to protect the rights of the accused. These amendments, such as clearly defining the scope and sequence of a search and seizure of property, as well as the rules governing arrests and criminal procedures help to protect the accused individuals in the country as well ensure that law enforcement officials are held to a higher standard for they are the standard. These laws are depended upon for those accused of crimes and govern the proceedings that determine the issue of guilt beyond a reasonable doubt. At the same time, even when these individuals are imprisoned, the 8th amendment helps to regulate the police's conduct in terms of application of punishment, preventing torture.
The 4th and 5th amendments are paramount in limiting police power for how they can treat suspects or those they arrest, or private citizens on the street. The 8th amendment also limits the use of force to what is considered "reasonable" for the situation a police officer finds him or herself in.
The Supreme Court, through its rulings over time, regulates the police by throwing out evidence gathered illegally, or as in the case of Miranda v. Arizona, freeing a suspect because he was not read his rights in a language he understood. They rule on acceptable police procedures, and what law enforcement actions are constitutional (wiretaps, surveillance, etc.)
The Bill of Rights, as interpreted by the Supreme Court and other courts, regulates the police by dictating to them what procedures they may and may not use in trying to apprehend suspects and gather evidence about them.
The most important part of the Bill of Rights in this regard is the 4th Amendment. Court interpretations of this amendment regulate when police need warrants to search people and property.
Another important amendment is the 5th Amendment. It is this amendment which gave rise to the famous Miranda case which requires police to read suspects their rights.
Neither Bill of Rights or the US supreme Court directly regulate the activities of police. The actual regulation of police, or for that matter, of any government institution or process are regulated by separate laws, rules and regulations, enacted separately for different fields.
The main purpose of the bill of rights is to ensure that such laws, rules and regulations do not violate the bill of rights. For example consider the fist clause of Bill of Rights forming the first amendment to the constitution. It says:
Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances.
Also the function of supreme court, in relation to bill of rights is to decide if any action by government or any law passed by the it violates the bill of rights. This is also done by supreme court only when referred it following the laid down procedures. In deciding on such matters, the supreme court also interprets the provisions of law that are open to ambiguity. For example, the fifth amendment uses the term "due process of law", which can be interpreted to mean different things by different people. Supreme court interprets and clarifies such provisions of bills of rights as and when required.