Hi M.,
It sounds like typical 3 year old trying her wings and seeing howo much control she has. Control of your environment is very important so make sure that she can control some things like which of two shirts she would like to wear, which fruit she would prefer, but do NOT give her control over things that she has no business controlling i.e. Do you want to come to the store with Mommy, or we are going to go to the store now...okay? If it is not a question don't present it as one, and if you are presenting her with choices, make sure it is a choice you can live with and honor.
As for bath time you can make it a choice if that is what you wish and give her showers of you can let her know in no uncertain terms that it is not a choice. BUT you can make it seems as though she has a choice by saying something like "I know you don't like baths right now, but you must take one. Would you like your bath with or without bubbles?" "Would you like your bath in the morning or at night"; if that is an option. Let her choose the washcloth etc.
Good luck!
T. Nelson