What with launches and unmanned rockets becoming cheaper and more the norm, and the rising worries about trash in the ocean and our orbit, why not just throw it at the sun and forget about it?
Fuel would be required for leaving the atmosphere, providing space positioning maneuvers, and some to turn the vehicle around and return to Earth.
A disposal ship could just use the momentum to release the trash compartment at the target (the sun), utilize rocket to turn around, and then slowly navigate home via solar sails. If multiple disposal ships are being produced, then we could have trash being disposed annually as these depart and return.
Also I stand by my idea of using Venus instead of the Sun since Venus is often closer to Earth than Mars due to our orbits. This would reduce fuel costs.
There are metric megatons of trash being produced on earth(I may be wrong on this but there is a lot). You'd need thousands of craft at the minimum to get the effect you want-that is cleaning the earth's land and sea of waste product, which is the point of this question.
That said Venus is an option as well-the extreme heat would melt anything we dumped there to a liquid compound in moments.
Venus is barely even a tourist trap. That's like going to New York just to see Staten Island or heading to Paris, TN because you wanted to see the Eiffel tower. If I'm sending my trash to space, then I want it somewhere premium so that I can be proud and dramatic about it.