I'm looking for the diameter of the connection point for both the clarinet and bass clarinet. The part in red below.
My research indicates that there are two standard sizes:
"The diameter of the bore is defined by the instrument (or better: its type), because the mouthpiece must have the same bore as the rest of the instrument. This is for example 15,2 mm (equals 0.598 inch) for a German style A- or B flat clarinet and it is 14,9 mm (equals 0.587 inch) for an A or B flat Boehm instrument, just below the mouthpiece."
(It is highly likely that if you aren't in Germany, you will be using a Boehm instrument.)
Further evidence for there being a standard fitting comes from various suppliers' online shops, where a range of clarinet mouthpieces are offered with no mention of different sizes.
I will be able to consult a clarinet player on the subject later today!
Laurence Payne gave the inner diameter numbers. In your image it looks like you're looking for the outer diameter.
I'm measuring my B45 (Bb clarinet) and EPE JM (Bb bass clarinet) mouthpieces with a simple ruler, so I can't give a sub-1mm accuracy. I'm reading 22mm and 30mm respectively. For comparison, the inner diameters are 15mm and 23mm.