I don't know if this is going to speak to many here, I hope it does, but it's good anyway in the process of trying to understand what dialectical science would look like, as opposed to our current outlook on science which is metaphysical.
By which I don't mean the scientific method, or scientists themselves, but science as a whole and as itself. If we hold that it doesn't exist outside society (and of course it doesn't), then science has a philosophical character. Metaphysics being the contradiction to dialectics, it's also not the philosophy of the bourgeoisie but rather the philosophy that was the most advanced, the most usable for people's needs, before we discovered dialectics. Much like we first learned to make stone tools before we learned to make them with metal, we first had to know metaphysics and idealism before we could know dialectics and materialism.
Today, science is taught metaphysically; it is seen metaphysically, it's practiced metaphysically, and we take that as fact. We have trouble seeing science any other way because this way makes sense to us, it's all we know.
If you were already aware of this character (studying in isolation, with observations and facts plucked out of their dialectical process and studied by themselves), this question should make sense to you. How do we rethink science in a way that is dialectical. Basically, in a way that we are still doing and studying science, but dialectically?
And of course I don't mean generalities like "it would be placing dialectics back in science", I want to see how far we can struggle with it.
Metaphysics, coming from the Greek words for "the things after physics," is something that by its etymology is literally outside of science. To understand where you're coming from, you'll need to elaborate on how you're defining "metaphysics" and how your conception of "science in general" is based in it.
There is no disentangling the scientific method from the term and our conception of "science." It is the cornerstone of the philosophy, and is inherently dialectical by its nature: it is a process by which a falsifiable (hypo)thesis is pitted against its antitheses through experiment and observation. The synthesis is a new, revised thesis that is again pitted against its antitheses in iteration. Its fruits are a testament to power of dialectics.
As others have noted, bourgeois decision making regarding the application of science does not tend to use dialectical analysis, but that is not unique to "science," and I'm not convinced that the decision making of the bourgeoisie is "metaphysical" in any essential way.