This doesn't quite answer your question but the Food and Agriculture Organization (FAO) has a global sediment yield database in the form of an Excel spreadsheet available here: http://www.fao.org/aquastat/en/overview/archive/river-sediment-yields although you should note that this was last updated in 2000.
This work see: https://csdms.colorado.edu/mediawiki/images/CSDMS_Tazmul_Poster.pdf may also be of use as well as this one: https://pubs.usgs.gov/sir/2010/5091/papers/Gray.pdf
Darren Lumbroso ,Thank you, Darren for the sources! The poster you refer to came our of our research group maybe two years ago. I'll take a look at the other two! Again, thanks a lot for your efforts!!
French colleagues developed a web application for calculation of bedload transport in mountain streams/rivers. You can find a lot of field and laboratory measured data in their "Data base" - https://en.bedloadweb.com/
Milliman, J.D., Farnsworth, K.L., 2011. River Discharge to the Coastal Ocean: A Global Synthesis. Cambridge University Press, Cambridge, United Kingdom.
Although no specific bedload data, it can provide you an overview of possible information sources.
We actually have two applications in France that address bedload caracterisation and transport at a national scale : 1) Bedloadweb (https://en.bedloadweb.com/) which provides a toolbox and data base on sentiment transport and its modeling. You'll also find in it data from US rivers. 2) IED Carhyce (http://194.57.254.11/IED/), which is a processing interface of data from the Carhyce field protocol (hydromorphology characterization of rivers). You'll find in it data concerning bedload at the stational scale (wolman is used to characterise surface bedload).