Yoyo: I can't say for sure that no flying ops took place to the east of the bridge but .. a couple of concerns I would have are; firstly, the bridge itself which, in my view, would have represented a 'snug' fit for the S23 .. tail clearance (especially at high tide) would (I imagine) have been a real concern.
Secondly, river traffic to the east of the bridge during the time of Shorts' stay in Rochester (1915-1948) would have been considerably busier than that on the western portions of the river due in no small measure to the bridge itself which served as a demarcation point for commercial activity with no ships being able to pass beneath it. Most of the materials for the 'Shorts Seaplane Works' were 'tugged' in lighters.
Of course .. some 10-15 miles to the east of the bridge is the Isle of Sheppey where the brothers Eustace, Oswald and Horace Short built their first aircraft factory!
Rochester Bridge .. depicting the somewhat limited clearance available for the Empire Boats to pass beneath
In your original post you mentioned the B-39 submarine. My UK sources inform me that she is still moored just east of the bridge and that within the past month she has been 'righted' having sported a keen list to starboard for some time.
The sub's owner has named the boat the 'Black Widow' (part of some sort of
PR campaign I suppose) and at one point she used to be open to the public. Some details
here and
here.
The B-39, a 'Foxtrot Class' Russian submarine moored to the east of Rochester Bridge not far from the site of the Shorts Seaplane Works