So hey, blog fodder!
Bleach has been running for about 15 seasons now, as far as I know, and has changed theme music many times. However, it doesn't change music specifically with the seasons. I haven't ever been able to figure out exactly why it changes when it does. Sometimes it seems the new music indicates a shift in the story arc, sometimes it doesn't.
Also, the theme music of most anime that I am aware of uses shortened versions of previously released songs. Bleach, for example, generally uses 90-second versions for the opening theme and 60-second versions for the ending theme. The opening is always a different song from the ending.
"Asterisk" was a 2005 hit by the Okinawan band Orange Range. Their music is sort of alt-rock with some rap thrown in (to the best of my knowledge). It went to #1 on the Japanese charts and stayed in the top 20 for 22 weeks. It was used as the Bleach opening theme for episodes 1-25.
Here's the opening theme version for comparison.
This is my favorite of all the Bleach opening themes so far, although I haven't heard full versions of them all yet. Here's the full version, official video with English subtitles.