You are correct in thinking that a load bearing wall would normally have a beam in the floor supporting it larger than double joists but you should figure out how the floor and walls above are supported before proceeding.

There are several variables in your situation.When was it built and what were the codes , if any , at the time. Codes change and I can tell you that in this state my 50 yr old could not be built today. Do a little leg work , make a determination of how this house was framed,top to bottom, develop a simple sketch and take it to a lumber yard. I say lumber yard (not a box store) because more than likely they will have professionals that can advise you. There are many factors involved that I won't go into.
Also be aware that this wall may contain plumbing and wiring. I love my wife but and some of her ideas, but her technical understanding and skills are nil.

A word of caution: don't take structural advice from anyone who has not actually visited your house and investigated the framing system or from someone without structural knowledge or make any assumptions based on when the house was built or what code was in effect. An experienced architect, engineer or builder should be able to figure it out with a minimum of demolition.