Well, this month just started, it's the 4th, so ofcoarse your bandwidth quota won't be anywhere near your max.
The size fluxuation could be solved by apache (the webserver) compressing its logs of your site at the end of the monthly cycle.
How the webserver handles logs logs is, they have a "current" log (/var/log/httpd.log for example), at the last day of the month this log is compressed (into say /var/log/httpd1.tgz) and new 0 byte file is created. Prior to compression this log could be any real number, i've had weblogs 80mb+ which would definitely be your problem here. Also, generally, they'll have it save a few log files (3-5 cycles worth)
(note that not all logs are compressed monthly, in fact I have them on my server set to cycle every other week)
All in all, 350mb webspace is quite puney... I can't believe there are actually hosts out there still which offer such small plans...
