Allow ice cream to soften. Make golf ball size balls from the assorted sherbets (use a tablespoon - they don't have to be perfect spheres). Place in freezer if they begin to melt.
Stir ice cream to a creamy consistency and spread about 1 cup of bottom of a 12 cup bundt mold. Place 1/3 of sherbet balls in mold. Top with 1/2 of remaining ice cream. With flat side of metal spoon press mixture into pan. Combine remaining sherbet and ice cream. Press firmly into place. Smooth top and cover with foil. Freeze. To unmold, dip in warm water and turn out on serving dish.