1978 Bedford bus Conversion
 

How do I identify the existing gearbox that is fitted to the OM352 Merc engine. See the project on Facebook under same name

The OM352 Merc engine is not original equipment AFAIK, so the gearbox might well be associated with the Merc engine rather than being of Bedford origin.

A mechanic familiar with either Bedford and/or Mercedes trucks might be able to recognise the casing (though there should be a plate attached which would identify the make and type).

Bedford used Turner and Eaton gearboxes in addition to their own, and Mercedes might have used ZF as well as their own.

Try lifting some access panels in the bus floor, or otherwise you will have to crawl underneath unless you have a hoist or a ramp/pit.

What model Bedford is it?

There should be a plate somewhere giving details of the chassis number if you aren't certain. You might have that information in the vehicle registration papers of course.