I would say that "force is a one-form" is a statement that has some truth to it, but it's somewhat context-dependent.
In any context where you have a metric, you can freely convert back and forth between vectors and one-forms, and the distinction between them becomes uninteresting. Examples of such contexts include relativistic spacetime and Newtonian 3-space.
If you don't have a metric, you can't do that. One example of this is four-dimensional Galilean spacetime, which doesn't admit a (nondegenerate) metric. Another example is when you're using generalized coordinates, as in the figure below. The angles $\phi$ and $\theta$ are generalized coordinates specifying the state of the arm and barbell. There is no metric defined on the $(\phi,\theta)$ space. As a function of these coordinates, you can define a potential energy $U$ for the system, which depends on the masses of its three parts (upper arm, lower arm, and barbell). The gradient of $U$ is a 1-form, and it represents the gravitational force on the system.
Another, similar example is that if we take the equation $W=Fd$ for mechanical work, clearly if $F$ is a scalar and $d$ is a vector, $F$ must be a 1-form.
So we have some contexts where there is no motivation for insisting that force is a 1-form, and other examples where there is very strong motivation. Note how your example of a magnetic force fails to fit into mold of the latter types of contexts. It's not derivable from the gradient of a potential (because it's velocity-dependent), and it doesn't do work on a free particle in the absence of other forces. On the other hand, it does fit nicely into the category of situations where the distinction between a vector and a 1-form is irrelevant. Electromagnetism is a purely relativistic theory with no useful, uniquely defined Galilean limit, so it doesn't make sense to talk about magnetic forces except in the context where there is a metric on 4-dimensional spacetime.