Can I put the bell tower card down if I don't have seven district's but another player does? I'm asking because I just played for the first time and I made this move and ended the game without wanting to be the winner by points.
If you can pay for the district card (and don't already have it in your city), yes, you can build it. You can do this whether or not you have seven districts and whether or not another player has 7 districts.
When you do, you MAY announce that the game will end at seven districts (but you don't have to).
Card text (from Dark City expansion version in 2008), emphasis added :
Purple - Cost 5
When you place the Bell Tower in your city, you may announce that the game will end after the round in which a player first places his seventh district. You may do this even if the Bell Tower is your seventh district. If the Bell Tower is later destroyed, the game end conditions return to normal.
If you do announce it, then yes, the Bell Tower in play and another player having 7 districts will end the game, yes.
If you don't intend to end the game at this time, though, you're free not to announce the change to 7.
EDIT: Regarding the "MAY" indicating that the effect is optional (see comments, where it was suggested that "not announcing would be so you could pull it out as a surprise, not that not announcing meant it didn't happen."):
Yes, not announcing it means not changing it. Otherwise it wouldn't be worded with "may announce" at all, but rather with something like: " The game will end after the round...seventh district. If the Bell Tower is destroyed, ... return to normal." (This would also run counter to every other district: there are no hidden effects. "play from the table, not from your chair" as the hustlers say.)
If you want to get really lawyery with the text, you could wrangle out that there's no change at all even if you do announce: the text allows you to announce but has no text saying that the rules actually change. (although it does have text that will "return to normal" from this non-change). No one but lawyers would believe that line of reasoning, of course, but it does help illustrate the effect of the text as written.
The only other place I could find that addressed the question (either in agreement with "optional" or not) is this post on BGG , which agrees:
The fact that the text says "may" indicates that using the district's ability is optional; however the fact that it says "When you place ..." indicates (to me) that you can only do this whan the district is built - if you don't do it then you have passed on the card's ability forever (well, for the duration of that game).