and the new bath is acrylic. Since there is there is very little
in the way of metal, do I have to bond it.

No. You wouldn't even bond a metal bath if the pipework is all plastic. Same
with radiators/towel rails. Don't bond unless supplied by metallic pipe (or
connected to structural metalwork/other possibly earthed item - very
unlikely in domestic building).

(*) the shower will have metal plumbing where visible (plastic where
not), but is driven from the boiler (i.e. is non-electric).

Basically, if the plastic supply length is greater than 1m and the metal
plumbing doesn't go where it might get earthed accidentally by something,
then it doesn't need bonding. 10cm of chrome where it goes into the wall to
continue thence in plastic, I wouldn't bond. This isn't a case of laziness.
It is SAFER not to bond in those specific circumstances.

Christian.