I also have some problem growing radishes. My guess is that these are planted too closely or the soil is lacking some nutrients.

A lot of my radishes came out spicy, but boiling them until they begin to pale takes the edge out and makes them tasty again.

Radishes like cool weather. Hot weather makes them bitter. Now thru September would be a good time to plant them. They do need to be thinned out. Also, if you have heavy or rocky soil it can inhibit bulb growth.

Concur with booberry, Radishes do well in the early spring and fall. It is not a summer vegetable. Salad Rose/Salad Giant( Burpee can't seem to make up its mind) It is a good 35 day radish, in my opinion better than White Icicle, which has the same date to maturity.
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They like cool weather and loamy soil with sufficient nitrogen in nitrate form for quick growth. Sandy soil doesn't hold nitrogen well. Our radishes don't bulb either. Then we planted in a new patch that was converted forest, very loamy soil, and - beautiful radishes, especially the fall planted ones. That's how an Ag. rep explained it to me about available nitrogen - hope I've remembered right.

As the above people mentioned - Radishes will begin seeding before their bulbs produce enough meet to eat during hot weather. I heard that some farmers use shade cloths and plant them in the coolest spots on their farm during hot months.
We plant ours in early spring. We haven't yet planted any in fall but Radishes have been a very good seller at our market and so we plan to this year.

Concur with generally useful advice above. I'll add that you want your radishes to grow as quickly as possible to be able to tolerate insect pressure, which can be intense. Even my best radishes tend to have some insect damage on the bulbs but a healthy, fast-growing radish will heal up those wounds quickly into a non-issue. In my case I'm fairly certain the Root Maggots were to blame.
I tried growing radishes in warmer weather and got plants that bolted *way* too soon.