Mint is by far, best contained.
If you bury the bucket do not be surpised to find that the mint starts to escape through the holes you made in the container. It spreads by the roots.
Better keep a big container on top. As a plant, it can last for years, an attractive pot is suitable. Cut it hard back in Late May early June and either make tons of mint sauce or compost it. Then use the new shoots.
I take a cutting and root it in water as soon as mint appears. Then pot it up for use during the short period between cutting it hard back and new growth. I always manage to find some one grateful for a 'mint cutting' in July when the new spuds are ready.
Mint is nearly as bad Horseraddish and Knitbone. They are all difficult to destroy and will take over.