Quick answer for how long does anesthesia stay in your body: about 24 hours.
Anesthesia is administered and used to control pain for medical procedures such as surgery or dental work. There are many different types of anesthesia (local, regional, epidural) which are administered in a variety of methods (respiratory gas and injection are the most common) in varying amounts depending on the severity of the medical operation. Due to the multitude of the drug, there is not a single definitive answer to how long does anesthesia stay in your system. A generalization of less than 24 hours is the collective time frame based upon the average half lives of different types of anesthesia.
For example, the drug Midazolam is a sedative drug that is regularly used as a pre-operative medication to promote relaxation, reduce anxiety and produce short-term amnesia. The amount of time it takes for the body to use and expel l the immediate drug is approximately 3 hours in a healthy subject. Therefore, more than 98% of the drug is eliminated from the blood stream in (3 hours x 5 half-lives) = 15 hours. From the collective list of frequently used anesthetics, not a single has lingering effects past 24 hours. Assume how long anesthesia will last in your system is less than one day.