The suggestions given are all good. The solution for you will depend on several things -- the type and size of the bushes, the location with respect to your buildings, the size and strength of your tractor/loader, and so on. Look at each post carefully and see what most closely resembles your situation. If you just have a couple of them near the house, I'd go with pulling either by tractor or truck with a long strap or chain to allow you to sit on pavement or at least a driveway so you don't tear up the lawn. If you're worried about the lawn and can't use the above option, do some digging first, water it all down good, and try the FEL methods.
For me here in the glacial moraine mix of soil types, Multiflora roses are the problem. Small ones yield to the FEL and teeth dig/pop method. Larger ones need a cable noose around the base attached to a chain and then to the drawbar and pull out fairly easily. My soils are mostly sandy clay loam, with some clay loam, some broken sandstone, etc. None of it is heavy soil like pure clay or gumbo.