Argument from Silence with Silence means consent

Argument from Silence is a fallacy because it entails presumption of whatever the proponent is asserting merely because it's not actively countered.

"Silence means consent" was a common law element asserted by Thomas More during reign of Henry VIII, not a construct of logic, and despite its wide acceptance, when it became convenient to do so, Henry disregarded it and pursued charges of treason against More when he would not affirm Henry's positions on divorce.   More thought he and his family were safe by never revealing what he thought.

More might have hoped to survive using “Qui tacet consentiret”, but he was doomed because his active opposition would have resulted in the same outcome.

To the point of the question, Jay never made an assertion of Bob's culpability. Bob's lack of response has no meaning, but if one could be construed it would be that Bob agreed that Jay could not find his keys.

It is still a problem because we don't know why the person is being silent, we cannot assume the reason is consent. It is like me sending an e-mail to the president of the USA asking if there are aliens that visited the earth, and finishing with "if you don't reply, I will just assume that means you are agreeing that there are aliens visiting the earth." Then after a few weeks concluding that I now have confirmation from the president of the USA that aliens have visited the earth.

"Silence means consent" is just an unsupported, arbitrary judgement. It doesn't affect the truth value of what is said (or unsaid), so you can't infer anything from this other than "Bob probably doesn't want to talk."

From the looks of this, Jay went into the conversation with a predetermined conclusion, and was simply seeking easy confirmation of this, hence the "silence means consent" point.