Bulma and Shadow's relationship

Shadow's opinion of Bulma
Shadow has some respect for Bulma, being the wife of Vegeta, but he doesn't fear her at all, unlike Vegeta who does to a certain extent (though far less so than most of the Z-Fighters and he is the only Z-Fighter who has able stand up to her  multiple times). Also, Shadow seems to be angered by Bulma's willful personality, kind of like how Chi-Chi's attitude angers Vegeta. Regardless, Shadow is usually not hostile towards Bulma unless he is angered enough by her. Shadow appears to get along with her more than he does with most others, and he sometimes praises her for her major achievments, but he is not afraid to belittle her for her shortcomings.

Bulma's opinion of Shadow
Bulma fears Shadow's temper, as when he gets angry he is notably more violent than Vegeta. She is also somewhat bothered by Shadow's tendency to speak his mind no matter who he is around, but she doesn't dare slap or punch him, as she fears he might retaliate in some way. Because of this, while she is clearly bothered by his attitude, she doesn't react the same way she would to most people if they spoke that way.