Warm-up sets aren't absolutely necessary, no. Some people go into the gym, load up their max, and manage to avoid injury for at least a while. But warm-ups are a tremendously good idea, because they reduce the likelihood that you will pull a muscle while lifting your max. You should get warm before lifting by running or, as you do, using a rower or elliptical, then put progressively more weight on the bar before your heaviest set.
If you're benching under 100 pounds I'd do one set with the bar, then one with 75 or so, then get right to the heavy sets. If you're not lifting very much weight, perhaps because you're doing sets of 12 to 20 for bodybuilding instead of strength training, then warm-ups aren't really necessary.