Definitely start with the idler pulley and tensioner pulley.

They are the same exact part number, so if you're low on cash you can replace the tensioner pulley alone without buying the whole tensioner. If you can afford the tensioner, it's best to replace the entire unit though.

If that doesn't solve it I'd give the alternator a really good listen. Squeaking like you described could be the first stages of a failing alternator bearing.

__________________
Current Bimmer
2004 X5 4.4i Sterling Grey Sport/Premium

Past Bimmers
1991 318I Alpine White
1995 740I Alpine White
1991 525I Schwartz
1998 323IS Scwartz
2004 330CI Cabrio Titanium Silver Metallic
1995 540I Schwartz
2000 Z4 3.0 Titanium Silver
2000 330ci Coupe Titanium Silver