Is it true that there is no true halachic time one must wait to eat dairy after eating meat for Ashkenazim? (Of course, eating it in the same meal is a sin, and is not allowed!) So by waiting 3 hours after eating meat to eat dairy, do I fulfill the Mitzvah of waiting between meat and dairy? Thanks!
The source you are looking for is the Rema's (Rabbi Moshe Isserles) commentary for Ashkenazim on the Shulchan Aruch. Yoreh Deah 89:1
It starts with the opinion of R' Yosef Karo (Tzefardim usually follow him.):
One who eats meat, even of a wild animal or fowl, does not eat cheese afterwards until he waits six hours. Even if he waits that period, if he has meat between his teeth he has to remove it. One who chews food for a child has to wait.
The Rema then comments by saying that some hold you do not need to wait any amount of time at all from meat to milk. Then he says the Ashkenazi custom he is familiar with in his locale is 1 hour. Finally at the end, he does endorse the 6 hour time frame used by R' Yosef Karo.
"...There are those that says that he doesn't have to wait six hours, but rather immediately if he finishes the (meat) meal and says the concluding blessing, it is permissible after wiping and rinsing his mouth (Tosafot Hullin 105a - "At the next meal", Mordechai chapter 25, Haga'ot Ashri, Haga'ot Maimoniot chapter 9 of forbidden foods, and Ravya). The simple custom in our countries is to wait after eating meat one hour and to eat cheese afterwards, but you have to say the concluding blessing after the meat (HaAruch, Haga'ot Shaarei Dura) because then it's like a new meal and permissible to eat according to the lenient view. But with no blessing, waiting alone does no good. It doesn't matter if you waited before the blessing or afterwards (his own reasoning, from the Mahari, as opposed to the Issur v'Heter). If he finds meat between his teeth after the hour, he has to pull it out (his own reasoning, from the Ran above). And there are those that say not to say the concluding blessing in order to eat cheese (Aruch in the name of Maharach) but we're not careful about this. And some are careful to wait six hours after eating meat before eating cheese, and it's proper to do so."
So the Shulchan Aruch does not mention a concept of 3 hours. It is either nothing, 1 hour, or six hours.
However, other authorities say or suggest other amounts of time in between 0 - 6 hours. If you just wanted to know if there is an opinion that you only need 0 or 1 hour for Ashkenazim, then yes, there is such an opinion. Your concept of 3 hours certainly fulfills the more lenient opinions which require less waiting time.
Origin (sources) of the three hour wait can be found discussed here:
As always, this answer is for learning purposes. If someone has a true question about how many hours they should or should not be waiting between meat and milk, they should consult their personal Orthodox Rabbi for guidance on what is right for them.