First, make sure you understand the differences between "pipe" and "tubing". Tubing comes in all sorts of sizes, shapes, and wall thicknesses, while pipe (which refers specifically to plumbing materials) is only made in certain standard sizes.
Pipe is not measured by actual ID, but by some archaic traditional system referring to the size that it was a hundred years ago when materials weren't as well understood and the walls had different thicknesses, but since then they've retained the same OD so that the thread size would stay the same while the wall thickness changed and the ID followed.
Thus, common sch 40, 1 1/2" steel pipe has an ID of 1.61".
Also, pipe comes in more than one standard wall thickness, while the OD stays the same, so the ID can vary that way, too.
Heavy-wall sch 80, 1 1/2" steel pipe has, coincidentally, an ID 1.50", but don't trust that because sch 80 3/8" pipe has 0.42" ID and sch 80 3" pipe has a 2.90" ID.
Additionally, pipes made of different materials have different sizing conventions, such as cast iron, copper, and various plastics.
Finally, pipe is not manufactured to extremely high tolerances, and usually has a weld seam and is a little out-of-round, so even the published dimensions can vary from the measurements of your pipe.
The best plan is to avoid plumbing pipe for fabrication jobs, and stick to tubing, which is labeled according to its actual dimensions. You can also get steel tubing made from better alloys than pipe, and made with different and better methods.
General-purpose bushings are usually manufactured to common unit dimensions, such as 1.5", 1.25", 25mm, 30mm, etc, and are intended to work with dimensional tubing and bar stock. You'll have trouble finding a bushing with such an odd 1.61" diameter, because plumbing pipe isn't intended for structural use. I looked at an enormous machinist supply mail-order company, and they don't offer anything even close.