I have heard of steroids affecting mood, yes, but a doctor or pharmacist will be able to give you better information. Have you had problems with your mood before you started taking the Budesonide? Can you call your GI about it and ask them?
It would depend on your dosage and what meds you take for Bipolar but yes, speak to your doc about it all. They should already have checked they were okay to give you while on current meds though. I can't speak for what it does to women but in me it felt like a boost of testosterone in that I was more confident, felt strong etc. It didn't raise my mood to anything like hypomania or beyond though. I also assume you won't be on them for all that long, just a couple of months maybe until your symptoms settle down?
PS: love the typo, but I'm not sure we all want to give our meds an ovation!