If I am remembering correctly the production of new Colt Bisley Models ended in 1912. There were probably spare barrels for a few years after that (warranty work & cleanup of old parts) but I think all distinctly Bisley parts, ie hammer, back strap, trigger guard, grips, trigger, and marked barrel were gone by the 1920s. All other parts were the same as the Colt Single Action Army. So to answer your question, no not likely.
I know this doesn't relate to your inquiry but I bought a Cimarron Bisley revolver in .45 Colt with a 4 3/4" barrel that is a fine shooter. To my untrained paws it looks and feels exactly like the Colt Bisley revolvers I've handled. Its action is very tight and its trigger drops the hammer with slightly more than 4 pounds of pull. It cost me a small fraction of the cost for a Colt Bisley revolver, but does not say Bisley on the left side of the barrel. I like it very much.
A few of those doing high grade SAA restorations usually do re-marking by using roll-dies on the bbl's address.
One that adv he has the Bisley bbl marking is Dave Lanara.
He's well respected in the restoration biz for his work on Colt Single actions.
SAA restoration work is never inexpensive.
Remarking bbl addresses with handmade roll dies included.
He currently lists a price of $150 to do the Bisley bbl address on your bbl sent to him detached and polished.
Scroll down to the Roll Die Stamping in the Restoration Services link.
That does not include the caliber marking on the side,,that's extra of course.
But this is Restoration work..
Sometimes it's better to keep an eye out for a 'take off bbl'.
But those are getting harder to find as time goes on. Those with a good bore even more so it seems.
Any 1st or 2nd generation Colt SAA bbl will fit the Bisley Model. The bbl threads are the same as were the dia's and the placement of the ejector housing stud.
The bbls just won't say 'Bisley Model' on them of course unless they orig came from one.
3rd generation Colt SAA bbls have a finer thread and will not fit the earlier 1st and 2nd gen Colt frames.