Hello,
I've read the same thing about betas over 1200 - they can take up to 3-4 days to double. Your numbers look good, from then on only time will tell. Also, you had a huge jump from 388 to 2052 in just 2 days, maybe your body is balancing out after that(??). I had a big jump from 337 (1st beta) to 1325 (2nd beta) and that was over 3 days, not 2, and my doctor still thought it was a great increase for a 3-day period.
Any particular reason your doctor's office is giving you so many blood tests? I know most doctors will do 2 at the beginning just to check the progression, and if all is good, they stop and just bring you in for a first scan between weeks 6 and 8. Some will do 3 to be on the safe side, but I've rarely heard of 4 blood draws for betas, unless there's a problem with the pregnancy. Which doesn't seem to be your case.
Like Juliet11, mine usually does two, and if the progression is good after the second one, they stop at that.