"put me down on the count" means your score, or in this case suitability for a job, is lowered. Bushwah is a way of saying Bourgeois, which is the middle class but in this form is a negative way of talking about behavior of the middle class. IE it's all a load of Bull $h^t that this speaker doesn't take seriously. While I'm not sure about the 'speed-shit' In this line, I guess it's just an exclamation to emphasize that the speaker doesn't think an arts education is very useful or serious.