A single teacher punching another? That's a bit thick! (10)

'bit thick' is the definition.
'boneheaded' can be an answer for 'thick' (thesaurus). I'm not certain of the 'bit' bit.

'a single teacher punching another?' is the wordplay.
'a single' becomes 'one' (a single thing - only one).
'teacher' becomes 'head'.
'punching' indicates putting letters inside (inserted letters punch or puncture others).
'another?' becomes 'bed' (I can't justify this - if you can you should believe this answer much more).
'one'+'head'='onehead'
'onehead' put within 'bed' is 'BONEHEADED'.

'that's a' acts as a link.

Can you help me to learn more?