Dear C.,
I'm not sure what you consider to be "on a budget" but in our world, a bounce house is extravagent, and not budget conscious. I've not seen any for less than $200! Besides, a one year old is too little for a bounce house anyways - is it for your 5 year old and her friends?
You know your child the best, but in my experience, one year old birthdays that include too many people and too much "stuff" don't go so well for the birthday child. Better to save this for when he is at least 3!
Be thankful and gracious for any birthday gifts your son receives (they are NOT necessary) and if there are duplicates or things you don't approve of, then donate them.
Happy 1st birthday to your son! C.