How much fuel does the A380 use for taxiing before takeoff? How much fuel does the A380 use for taxiing before takeoff and after landing? What does it cost at today's pricing?
Fuel burn
To be meaningful it's best to compare it. It is approximately 4 times what an A320 needs. So if both planes are fully booked, then in theory each passenger should pay the same for the taxi fuel -- it would become an issue though when the A380 has a low load factor.

Taxi Fuel is 1 170 lb for an average taxi duration of 12 min.

While for 12 minutes an A320 needs 300 lb.
Cost
As of 20 April 2018, it would cost Emirates -- the largest A380 operator -- about \$360 for a 12 min taxi in Dubai (less than a dollar per passenger).
But Dubai is a busy airport and as such the taxi duration can exceed 12 minutes. For example Emirates 203 from a few days ago had a taxi time of 30 minutes. Operating a large airplane at a busy airport has its costs.

References:

Airbus FCOMs for the A320 and A380
IATA fuel monitor (jet fuel cost varies by region).