Does one "speak" a sign language?

Solution 1:

One of the meaning of speak is:

• To convey by nonverbal means: His eyes spoke volumes. (The Free Dictionary)

• To speak is commonly use to refer to sign language

Ngram: speak, talk sign language:

• Cobb, who can read and speak sign language (which he learned from his deaf father), has been assigned by the department to assist Tess in the field as her investigator and interpreter when she questions suspects in a case. Stories relate ...(Encyclopedia of Television Shows, 1925 through 2010, 2d ed. Di Vincent Terrace)

• ... competency” as described above. Hearing children of deaf signers often speak sign language extremely fluently, suggesting that there is no neurophysiological reason for it to be difficult to be fluent in 3. (Artificial Sight: Basic Research, Biomedical Engineering, and Clinical Advances)

Solution 2:

I speak BSL.
I sign BSL.
I use BSL.

These are the idiomatic collocations you can choose from.