An easy split at Chester saves around £5-6.
Liverpool-Chester £2.90 SDS x2 = £5.80
Chester-Pwl £22.05 SVR
TOTAL: £27.85
Alternatively:
Liverpool-Bangor (Gwynedd) SVR £15.40 no restriction
THEN:
Get the number 5 bus to Caernarfon. (Arriva)
Then get the number 12 bus to Pwllheli. (Clynnog & Trefor)
If you get the connections right, then you are looking at 1h30 between Bangor & Pwllheli.
Bus fares only available as singles, and in total, one way, you're looking at £10.
TOTAL: ~£35.40
THE CHEAPEST (and very slow) WAY:
Get a Liverpool-Chester SDS @ £2.90
BUS: X94 Chester-Dollgelau (Arriva - North West & Wales Day ticket £5.50)
BUS: X32 Dolgellau-Aberystwyth (covered by above day ticket)
BUS: Aberystwyth-Pwllheli (covered by above day ticket)
IN TOTAL, SINGLE, £8.40, £16.80 return
If you wanted to reduce the cost even more to just £5.50 single, you could get the Arriva 401 bus from Liverpool-Chester instead. You get all the way to Pwllheli by Arriva, but expect to be on buses for about 6-7hours. For a fiver though it's a bargain.