。
She asked me a question without being shy.
Literal
She [topic-は] shy-act-not [without-ずに] me [to-に] question [object-を] did.
恥ずかしがらずに uses ~ずに ('without doing'), the classical negative te-form. 恥ずかしがる means 'to act shy / show signs of embarrassment' (using the ~がる suffix). So 恥ずかしがらずに = 'without showing shyness.' The ~ずに form is more literary than ~ないで but common in written Japanese.