I have loads of trouble with smbc, but american buttercream I can do pretty well. With american buttercream (ie powdered sugar kind) I just keep the speed on the lowest once I start adding the sugar.
I try to mix on the lowest speed also.
To help get most of the air bubbles out of this batch. Take a large rubber spatula and "smoosh" the icing from the middle pressing it against the sides of the bowl. (don't you love the technical term 
) Just keep flattening it with the spatula and it should get rid of at least the big bubbles.
HTH
Look up Sharon Z's (aka: SugarShack) U.Tube videos and posts on this board. There is a ton of them regarding her methods & recipe for b'cream. One of the most helpful tips is to be sure your batch fills the bowl - at least covers the beaters and slow, long beating.
Oh yeh, (I think it's) Serious_Cakes also has some U.Tube videos on making smooth b'cream.
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