It is typically a full day or a day and half to get an engine on the dyno, run it and then pull it off. It may sound like fun work to some, but it really isn't. It is a lot of hot grunt work and it all has to be done correctly or else you can destroy an expensive engine in a hurry.

Asking about cost is fine but you really need to get one level deeper with your questions. Does the shop have headers that fit your Hemi? If not, do your car headers fit their dyno? If not then you'll need to spend another $500 for dyno headers. Which carb and ignition system are you going to use? The dyno shop typically will have a fuel pump, ignition system and carb that are known to work. If you drag your stuff in there you could add some time and money to the job. I'm sure everyone is going to shocked to hear that most carbs that people bring to dyno sessions are down on power compared to the dyno shop carb. Everyone thinks they know how to tune a carb but I've sat in on at least 100 dyno sessions over the past 20 years and rarely does a customer carb work great. The best approach is to use the dyno carb to create a baseline then try your carb to see how far off it is. Then spend some time trying to get your carb dialed in. But this approach adds a couple of hours to the dyno session so now your cost has gone up.

Other things to ask about is how much data will you get. Does the shop use O2 sensors? EGT? Airflow turbine? etc. It all depends what you're trying to accomplish. A street car probably only needs a basic run stand type of test while a serious race engine can benefit from hooking up all the sensors.