Borel subgroup is conjugate-dense in connected algebraic group

Statement over an algebraically closed field
Suppose $$G$$ is a connected algebraic group over an algebraically closed field $$K$$ and $$B$$ is a Borel subgroup of $$G$$. Then, $$B$$ is a conjugate-dense subgroup of $$G$$, i.e., we can write:

$$G = \bigcup_{g \in G} gBg^{-1}$$

Statement over an arbitrary field
The statement as made over an algebraically closed field does not work over an arbitrary field, but we can make suitable modifications and make sure it does (can we?).