"Blast radius" is a very imprecise term, because one only cares about damaging amounts of blast. In a sense, the planes were within the "blast radius," in that they did interact with the shockwave, but they were sufficiently far away that all this did was bounce the plane around a bit, not destroy it. The initial shockwave from the Hiroshima bomb, for example, was powerful enough that the people on the plane initially thought it was flak, and the plane's accelerometer registered about 2.5 Gs — pretty significant. There was a second shockwave (reflected off of the ground) that hit 2 seconds later.

But to your main question. The question of how you drop an atomic bomb without killing the crew of the plane delivering it was, of course, considered very carefully by the scientists who designed the atomic bombs and planned the operations. The planes had very specific instructions about what speed and altitude they needed to be when dropping the bomb, and what to do after dropping it. After dropping the bomb on Hiroshima, they had about 45 seconds before it went off, owing to the fuzing equipment on the bomb that was designed to set it off when it hit the desired altitude above the ground. To maximize the distance between the plane and the bomb, the pilot made a sharp, 155º diving right turn (the bomb would be, for that 45 seconds, not just moving downwards, but moving "forward" along the original vector of the plane). They continued turning until they were traveling 180º from the bomb itself, at full speed. At the time the bomb exploded, they were about 10.5 miles away from it (slant range — the bomb was both further away horizontally and vertically from them). I haven't run the math to see if that makes sense (the max speed of a B-29 is about 350 mph, but you have to take into account the speed of the bomb moving laterally, the speed of the bomb moving vertically, and the speed of the plane as it turned), but it sounds about right.

For a weapon the power of those in World War II (15-20 kilotons), being 10 miles away is sufficient to not suffer damage. Again, it is still within the "blast radius" in the sense that a shockwave will (after a few seconds) slap into you. But it will be a shockwave significantly weakened by its transmission through the atmosphere.

Now, you might have a follow-up question: what if the weapons were much larger? How would a crew survive something like a multi-megaton bomb? (The largest nukes deployed by the US during the Cold War were around 25,000 kilotons in yield, and also dropped by bombers.) The answer is two-fold: 1. you increase the time it takes for the bomb to get to the detonation altitude, which can be done multiple ways, but multi-megaton bombs usually had massive parachutes to slow their descent, and 2. you increase the speed of the planes (those big bombs were dropped by jet aircraft that could fly nearly twice as fast as the prop-based B-29s).

Note that the bombs of World War II did not have real parachutes; they had squared ends (informally called "California parachutes") whose real purpose was to try and keep them from turbulently rolling as they descended (which could damage or unhook their delicate electronics). (It an interesting aside that Japanese accounts, including fictional ones like Barefoot Gen, often erroneously give them cloth parachutes. This is probably a confusion caused by the fact that when the bomb was released, another B-29 in the area released blast-recording instruments on parachutes nearby, and some of the eye-witness accounts confused these with the bomb.)

Interestingly, one of the problems with very large bombs, like the Tsar Bomba, is not the blast wave (a plane in the air can ride out a lot of turbulence, and they did get a lot of turbulence), but the thermal radiation, which for weapons in the tens of megatons can burn at huge distances. The plane used for the Tsar Bomba (and several other megaton-range Soviet tests) were painted a highly-reflective white to help shed some of that heat, but the crews inside of it reported it getting uncomfortably hot nonetheless, causing some of the dust within the plane to flare up briefly, creating smoke inside the cabin, and giving the tail gunner light burns. And this was all with a bomb parachute of unprecedentedly large size.

Anyway. Long story short, this is all a very solvable technical problem, even for very large bombs, although it is probably possible to make a bomb that is large-enough that dropping it out of a plane would not be feasible. But the bombs of World War II were not anywhere near that large.

For the details of the Hiroshima bombing, the late John Coster-Mullen's Atom Bombs has the easiest-to-access details of this sort, if one has a copy, and is where I got the report on the Enola Gay's conditions and distances at detonation (John loved this kind of thing, and interviewed the pilot and other members on the plane, as well as compiled a pretty comprehensive account of speeches and talks they gave afterwards, where some of those numbers are from). The discussion of the Tsar Bomba's conditions inside the cabin come from an article that came out in Russian some years back that involved interviewing some of the participants, which I probably got from Eastview while I was researching an article I wrote on the Tsar Bomba: Nikolay Cherkashin, "Political Secrets of the Age: Khrushchev did not agree to 'Armageddon,'" Rossiiskaia Gazeta (20 November 2000).