Where can I find data on bilateral trade? Where can I find data on bilateral trade between countries in the world over time?
I heard that only International Trade Center has access to this data, but I guess there's a public source. I tried but didn't succeed, for example this one.

Many thanks.
For aggregated trade, there is a excellent database from CEPII called histtrade. It covers data from the first industrial revolution. The site also has data covering disaggregated  trade but only with limited observations. 

http://www.cepii.fr/CEPII/en/bdd_modele/bdd_modele.asp

A second data set is the Barbieri Data set, that can be downloaded from the COW project. 

http://www.correlatesofwar.org/data-sets/bilateral-trade