Finding (correct) citation info for math references I've just recently learned about BibTeX, rather than manually making a bibliography at the end of everything I write. Now I'd like a reliable source for the citation info.

At school I can use MathSciNet through my university's account, but at home I cannot access that. I have been using Google Scholar to find citation info in BibTeX format but I find that very frequently the year listed is wrong, so I need to dig up the article and double check everything. Just to take the most recent example Lectures in Hyperbolic Geometry by Benedetti and Petronio is listed as having been printed in 2012, but in my copy of the book it says 1992. 

Perhaps it is giving me dates of reprints or something, but that is no good either. Having the date of the original publication is important when surveying the historical context of one's work, which is especially relevant to what I'm writing lately.

Is there a more reliable database for BibTeX-formatted citation info on math articles, which can be accessed for free?
For mathematical articles I'm not aware of any citation database of (nearly) as good quality as MatSciNet --- your university is probably also paying a significant subscription fee for it.

As Paul Garrett already mentioned, you can probably access it from home via your university's library. There is actually an even simpler method (at least with a laptop): while at your university you can "pair your device" to automatically have access under your university account for 90 days, when you need to repair it. See the green/blue icon in the top-left corner of MathSciNet, linking to http://www.ams.org/pairing/pair_my_device.html

If you have a desktop at home, you might also do this though a VPN or library site of the university, and then you're set for the next 90 days.