To 'bulldoze' means to either:
1. Push something with a bulldozer.
2. To bully or intimidate someone.
This latter meaning was actually the earlier one; the popular use of the term bulldozer to mean a type of tractor is comparatively new.
Bulldoze comes from the slangish term "bull dose" -- a dose strong enough to control a bull. In this case the 'dose' was a dose of violence; most likely whipping, but in fact nearly any sort of violent intimidation. It could be either a noun or a verb -- one could bulldose someone, or one could give them a bulldose.
The term first came into popular use during the run-up to the 1876 US Presidential Election. The radical Democrat paramilitary groups such as the Red Shirts and the White League would intimidate or attack groups that were likely to vote Republican -- and one of the newest and largest groups with this unfortunate tendency were the blacks, who had recently been given citizenship and the right to vote. In Mississippi's 1874 election the black vote had been able to soundly trounce the previously strong Democratic party, and in response the party developed "the Mississippi Plan', organized groups that would patrol black neighborhoods and farms, beating, whipping, and murdering hundreds. They also, during the 1875 Mississippi election, physically blocked access to voting stations, with violence as necessarily.
In 1876 this sort of violence was well known, and was brought sharply to the public's attention by the presidential election, which promised to be a close race. Throughout the South, but particularly in Mississippi, Alabama, South Carolina, Louisiana, and Florida, gangs were encouraged to take matters into their own hands, and make sure that Republicans did not make it to the polls.
The press started to refer to these practices as bull-dosing; this carried the subtext of 'excessive force and violence', and was probably used primarily by northern reporters who disapproved of these methods. The term gained in popularity, as the public loves a cover-all term -- whether hundreds of blacks were being massacred or one sharecropper was being intimidated, it was all bulldozing.
From this the term eventually came to mean any case of overcoming an obstacle through brute force. Over the decades, and against all logic, a term used to refer to the violent oppression of large segments of the population came to be acceptable in work, sports, and home life. And when, in the 1930s, a specific type of tractor blade had established that it was here to stay, it came to be known (first informally, then universally) as the bulldozer blade. This was eventually generalized to refer to the tractor as a whole.