Dismissing an argument/position by claiming implicit bias

A factual claim I made was recently dismissed on the grounds that "all persons have implicit bias" therefore "the claim you make cannot be assessed". An additional premise was that the other person did not claim I had a specific bias that this person had revealed. The argument rested solely on the general observation that "we all have implicit biases". The argument can be rephrased as: "Since we all have implicit biases any factual claim will rest on a biased observation/sample, therefore the factual claim cannot be assessed"

One candidate could be the "Bias fallacy". But this fallacy is to claim that someone is wrong on the grounds that they are biased. In my case the other person never claimed I was wrong, only that the truth/falsehood cannot be assessed since "we all have implicit biases".

Another candidate is simply an ad hominem, but then ad hominem becomes very wide. 

That is part of a category of fallacies, where the form is:

You are wrong because of [reason that has nothing to do with the facts of the claim].

As you correctly point out, this is an ad hominem (abusive) or even a genetic fallacy . It could be that they are biased, ugly, stupid, old, young, or have bad breath. The key to responding to such a claim of bias is to simply evaluate the claim on its own merits, independent of the source. Is this form common enough to warrant its own named fallacy? Maybe.

What I'm seeing here is that the person is avoiding the issue . They are making a deliberate attempt to avoid the argument you've presented, and have instead shifted to a different argument of whether or not it's possible to evaluate why claim objectively at all.

One caveat, though, is that depending on the initial statement you made, that might be a valid criticism. For instance, in scientific research, there is a lot of data that does require some subjectivity in its measurement. Consider the statement "54% of test subjects reported feeling less anxious while taking X supplement". 54% is an objective measurement, but anxiety is a subjective feeling, so it's difficult to tell based on that statement whether X supplement is effective for treating anxiety.

That said, it would really be on the person responding to you to elaborate on how bias would muddy the data supporting your argument if they wanted to be persuasive.

I want to say that it is a bit of a non sequitur 

As the existence of bias (which can almost always be argued given the broad definition of bias) doesn't preclude the argument of claim from being correct. Strictly speaking, bias itself has nothing to do with the factual claims of the argument. Though, naturally, it is grounds for healthy skepticism.