You cannot bear testimony in my opinion. You give testimony.
"Thou shalt not bear false witness against thy neighbour" = you must not give false evidence against your neighbour.
The obsolete character of the context in my quotation is the tipoff: bear witness is archaic. You still run across it and it still means testify, but it is increasingly rare. I think it is dying out.
I suppose the noun witness must have had the meaning evidence, but that meaning is surely obsolete outside the phrase bear witness. A witness in any other context is a person.