If someone gives consent to search your their car, can they search someone elses bag in that car?

If you give them permission to search your car, they can search everything in your car. If you give them permission to search your home, they can search anywhere. If Susan is there, she might tell them she wants a warrant for them to search and keep the person on her person. You can't give permission to search Susan, but only your car. So she better hold her bag if she doesn't want it searched. Might take her in anyway as then could have reasonable suspicion possibly.

Yes. If the bag is on susan's person though, they cannot search it.

It is a toss up,but Bob can only give permission for the police to search his car without a search warrant,but not Susan's purse. However,recent court rulings allow the police to search everyone in a vehicle (even for a traffic stop) regardless of any criminal record or not (they are guilty by association). The police can only (Constitutionally)search you or your property without a search/arrest warrant if they actually witnessed you commiting a crime,other than that-they have to have a search /arrest warrant naming the place or person to be searched and the items to be searched for or the person to be arrested. That has been tossed aside by the courts,just like reading you the Miranda - they don't have to any more and you have to ask for a lawyer,other wise,they can question you all they want.

I think they do.

Bob can give consent to search his property, not someone elses especially when it is obvious that it's not Bobs stuff. Now, if Sue gave permission to search her car and Jane's purse got searched too by mistake it would be for the Court to decide if it was a reasonable mistake, especially if evidence was found.

Anything in the car is fair game. If you didn't want it searched you should have not been in someone else's car.