It is known that knot groups are right-orderable, and that many of them are not bi-orderable. Here we show that certain fibred knots in $S^3$ (or in a homology sphere) do have bi-orderable fundamental groups. In particular, this holds for fibred knots, such as $4_1$, for which the Alexander polynomial has all roots real and positive. This is an application of the construction of orderings of groups, which are moreover invariant with respect to a certain automorphism.