I have both a Bernina 1230 and a Bernina 440 QE. I rarely have any issue with winding my bobbin like your picture. If I see it start being uneven, I do what a few others have suggested and use my finger to control. By the way I see you have an aurifil thread spool on your Bernina and I use that same thread frequently but have a spindle on the 440 QE that sets this type of spool upright and I also have a totally separate spindle that I use when winding bobbins from a large cone but using one of my Berninas to sew.
I agree with Pocoellie and would follow through with her suggestions. Bernina's are a great machine but pricey. Kelela