No.
NT40/CAT40/NMTB40 is much larger than the R8.
Here is a side by side of a R8 tool, NT30, and NT40 tool. As you can see NT40 tool is quite a bit larger than R8.
View attachment 333409
And a bridgeport head probably does not have enough room to accommodate a NT40 spindle as the spindle needs a minimum diameter (the quill part) of around 3.5 inch (my mill has a quill diameter of about 90mm, so around 3.5 inch or so) because you need room for the spindle, the quill, and the various bearings. R8 is simply too small. NT30/NMTB30 would be a possibility if you can find a spare spindle to use.
If you have a bridgeport series 2 mill, then NT40 spindle may be a possibility, as they have a larger head.
Also a NT40 spindle (if you have not already found out by now) is much heavier than a R8 spindle.
Edit: So they do make NT40 spindles for Bridgeports... Found this on ebay
Bridgeport Milling Machine Tools NT40 Shaft Spindle Vertical Mill Parts | eBay
You'll have to figure out how to change the spindle and use the right bearings... I don't know if its original bearings will work as this spindle looks a lot beefier compared to the R8... But NT30/40 is a great spindle because they have positive drive keys whereas R8 does not. Also they are interchangeable with every other milling machine as all the various -30 -40 taper is the same. Meaning if you have a CNC machine you can just cut the knob off the NT40 tool holder and stick a pull stud in it, and it will work in the CNC. R8 is manual mill only.
1Set Bridgeport Mill Part Milling Machine NT40 Spindle + Bearings Assembly | eBay
NT40 spindle with bearing. You are going to want this as the spindle is quite a bit larger than the R8 spindle... so your stock bearing will not work.