Bill's regular companion in lovemaking? (3)

I believe the answer is:

coo

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'bill's' is the definition.
The definition and answer can be both to do with communicating as well as being verbs in their base form.
Maybe you can see a link between them that I can't see?

I can't explain the rest of the clue.

Can you help me to learn more?

(Other definitions for coo that I've seen before include "Murmur amorously" , "Soft murmuring sound of a pigeon" , "Surprised expression" , "Make loving sounds -bill and . . ." , "Dove-like noise" .)

I've seen this clue in The Guardian.

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