Depends on how much power you want to lose
Based on the information in this answer, assume we need a minimum founder population of 400. Other answers suggest as low as 80 with good medical support, but that seems like it will be unlikely in your scenario.
35 of those 400 are your super-powered individuals. However, to prevent the genes from being too diluted, you need to spread that genetic variation among multiple generations. Lets say that every generation, you add ~30 new people into the breeding population for 12 generations. These people will bring their 0% power genes into the collective gene pool. Lets further assume that there is a 50% increase each generation: 3 children for each 2 parents. Here is how the gene pool looks each generation:
Gen Pop %Powerful
0 35 100
1 97 53
2 191 41
3 331 36
4 542 33
5 859 31
6 1333 30
7 2045 29
8 3113 29
9 4715 29
10 7118 28
11 10722 28
12 16128 28
13 24237 28
28% is the asymptotic limit. Your population will stabilize there in time.
Now lets re-run the exercise, but breed in far fewer people each generation; only 10. It takes 36 generations now (actually kind of a long time, something like 900 years) to get enough people into the gene pool, but on the plus side you keep the power a lot stronger. For this second run, we'd have to tone down the birthrate some to keep from over-running the earth, but the asymptotic power level is 54%. So the slower you add people to your gene pool, the more power you can maintain.
So the answer is: As low as 10 generations, if you don't mind getting depowered, around 30 generations to keep the average power level to 50%
Good old fashioned racism will help keep your population powerful
There is another factor at work. The superhumans will presumably be ill-disposed towards those who show few powers due to the genetic lottery. IF they discourage those people from mating, then your powers will eventually be bred back into the population. If, once the population has expanded enough to minimize the genetic bottleneck, people with less than 50% power are simply kicked out of the ruling class and now allowed to intermarry any more, you will find that the average power level of your group will increase over time; to at least 50%.
Thus, you may only have to interbreed for the 10 generations, and then rely on 'artificial selection' to keep your power level higher. With enough time (and enough racism) you can get your power level back to near 100%.
An excellent example of this in practice is the country of Mexico. For 400 years in Mexico, everyone in the upper class insisted that they were all Spanish, and didn't have any Indian in them. The result is that even though the population has a pooled genetic material that is about 30% European, 65 % Amerindian, 5% Black, the skin color skews heavily white (graph shown on the link). This is basically because skin color is the easiest thing to be racist about, so there was artificial selection pressure for lighter skin for so long. So there are now a lot of light skinned half-Amerindian Mexicans running around.
You can use this effect to eventually (maybe after 400 years) get a population of 100% superpowered half-non-powered (muggle?) people running around on your alternate Earth.