english ivy is generally grown as a ground cover where as hops grow from a primary crown and will only spread if you allow them to. strategy for keeping them contained can take many forms and the 'bucket' idea, as david mentioned, is an excellent method. if you grow them without the bucket it's best to:
1) grow them in an area that is accessible from all sides (not up against a wall or some other permanent structure). this will allow the crown to be pruned each spring to keep any rhizomes from creeping outward and establishing plants away from the main crown.
2) make sure the planting area (at least 3ft. x 3ft.) is clear of all plant material such as weeds, grass etc., and keep it that way. if a new shoot pops up away from the crown, you'll be able to see it and dig it up before it has a chance to establish. think of these shoots as the support wires of an upside down umbrella. they emerge from the crown in a radiant fashion and can easily be severed by placing a shovel in the soil between the tip of the shoot and the crown and then lifted and destroyed or relocated as cuttings. if you allow grass or weeds to grow up to the crown you can easily miss a new shoot poking up as it will utilize the surrounding vegetation as cover and be able to establish itself.
these are the two biggest 'must do's' that i have found to make it easy to contain a crown so you'll be able to dig it up without leaving any vegetative material capable of regenerating in the future. hope this helps, and hop to it!