Bosozoku or Bousouzoku would be the correct romanization.
Bousouzoku literally means wild running tribe, and refers to the crew/team/community. Yanki (or more accurately yankii) refers to the style/culture that is embraced by those in the Bousozoku community.
So someone in a bosozoku would embrace yanki culture, whether it's yanki style dress, yanki style cars, etc. Yanki is an adjective, bousozoku is a plural noun. You wouldn't say someone is a bosozoku though, it's a collective.
I've always understood Bososuko to be a gang that disrupted the peace with noise. I was almost positive it started with biker gangs who were lower rungs of the Yakuza, and then flared out from there.
However, a lot of guys on another forum I frequent consider Bososuko the opposite of Hashiriya. In other words, they're racers who have no concern for other peoples' safety - i.e. racing in traffic, etc. Hashiriya is the opposite, which obviously means they take responsibility for their actions, and even though the racing is dangerous it doesn't involve innocent bystanders.
I suppose "Bososuko" can be interpreted a few ways but it always tends to have a negative connotation to it.
I've always understood that those cars were considered "Yanki" style as well.
It's funny - Bosozoku has a tough guy, cool image, so the Japanese Gov't was actively trying to get the populous to change to call them Chinsoudan literally strange running group to make them sound less cool. It's interesting that the Japanese wikipedia site compares them to the Hell's Angels, with the difference being HA being older adults.