I found another one today:

Roblin 35237 : H pre 1899.

A this point I believe the following:

Bernard made barrel assemblies that he sold to gunmakers.
These sets included the tubes, lumps, probably the forend loop and for sure the bottom short rib.

It turns out that other barrel makers have been doing the same. For instance Heurtier was producing barrel sets which were silver soldered in their factory.

The barrel numbers are on the bottom short rib with a sequential number and a date separated by a dot.

The date was replaced by a letter at some point in the 1880s or 90s. This makes sense as the makers might not want a barrel date older than the gun manufacturing date.
I don't have example of all the letters, so I don't know if they were all used.
I suspect that H might be 1896 or 1897.
If a straight alphabetic order was used, it would have started in 1888 or so.
If you have Leopold Bernard barrel tube sets, please look and report.

All the best!
WC-