There is no direct bus from Duquesa to Gibraltar. You would need to go to either Estepona or Marbella to pick up the direct bus, or from Estepona, there is also a slightly tortuous stopping bus. Both these buses go to La Linea bus station, and from there you need to walk to the frontier (five minutes). You can't really miss it as there is a dirty great big Rock in front of you.
This is a link to the direct(ish) buses. Note there is an error, it does not take 1:30 between La Linea and Estepona. It is more like an hour. A return ticket is 4.88€, so Duquesa to Puerto Banus would be pretty similar, probably singles as it will be a stopping bus up and down the coast.
No idea about taxi prices, sorry can't help there as I always use buses.
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