The chances are the bumper is one of the models with cast in clips that capture the ends of the shock absorbers that mount to the body frame. Over time, especially on the side of the exhaust pipe, the mixture of road salt, Diesel exhaust and road debris creates a fairly vigorous aluminum eating coating, and the clip gets completely eaten away. Once this happens the bumper falls off and you cannot re-attach it without fabricating a new clip. I have done this with aluminum angle iron on my 1982 240D, but it never lasted more than a few years. In the end, I got an older bumper in good shape that has a different set up. The bumpers were interchangeable, but the one I got came with the shock absorbing struts on it, so I just unbolted the three fasteners on each shock, pulled the old one and inserted the "new" one.
So, look the inside of the bumper over and if there are no integral clips left, you need to buy a new bumper. If there are clips you take the three bolts out of the shock mounts, fit the rubbery end into the bumper clips (they slide in from the side I believe) and then mount the bumper back on the car by sliding the shock tubes into the holes in the rear of the car, and lining the bolt holes up for the three bolts. Insert and tighten the bolts and you are done. Good luck! Jim
1986 Euro 190E 2.3-16 (291,000 miles),
1998 E300D TurboDiesel, 231,000 miles -purchased with 45,000,
1988 300E 5-speed 252,000 miles,
1983 240D 4-speed, purchased w/136,000, now with 222,000 miles.
2009 ML320CDI Bluetec, 89,000 miles
1971 220D (250,000 miles plus, sold to father-in-law),
1975 240D (245,000 miles - died of body rot),
1991 350SD (176,560 miles, weakest Benz I have owned),
1999 C230 Sport (45,400 miles),
1982 240D (321,000 miles, put to sleep)