I haven't shadowed a general dentist, only in dental school clinics, about 3 hrs per week.
I know you're concerned with acing the DAT but, shadowing a dentist for only a month (After the DAT on 3/30, you would only have all of april to get to know them before the May 15th deadline), I don't think they would be able to write a very good recommendation letter for you. Besides, adcoms look for students who have built a relationship with someone over a long period of time. I would try to start now, only 3 hrs a week if thats all you can do.
Do the math- at about 3 hrs a week for the next 17 weeks or so, thats 51 hrs.
Most schools recommend/require 50hrs of shadowing so you'll have satisfied that and have come to know the dentist better, allowing them to write you a better letter of rec. Also, I don't think 3 hrs a week will cut into your DAT studying too much.
Best of luck.