There is a lot of misconception about " 60° ".
AS an absolute, you do NOT have to have 60° bushings to turn TBC. JohnnyCNC makes and sells the finest bushings you can get. His bushings are chamfered to 60°, so with his, they will match the 60° live center and dead center. But even if you are using 60° live and dead centers, it is not necessary to have to have a 60° bushing. More on this in the 3rd paragraph.
You can use standard bushings that are used on mandrels - I, and others, used these long before John started selling his 60° bushings. These mandrel bushings as a whole are not as good as John's but some work reasonably well.
Unless you are using John's special bushings or using someone elses or your own that have been chamfered to 60°, you don't even need 60° live center or dead center. Here is a link to a dead center that I made back in '07 that I used with non-60° bushings that were made for mandrels.
http://www.penturners.org/photos/images/940/1_Dead_drive_2.jpg
It is obvious to the naked eye that it is not 60°. I used this dead center for a couple of years before getting one from Grizzly and one from somewhere else. (Little Machine Shop? maybe.)
Mandrels have a dimple on the live center end that does require 60° live centers. Some people falsely transfer this idea to the TBC requirements. It is not necessary - unless you buy or make your own chamfered bushings that are 60°. But your quesiton was about 60° bushings, so the answer is no.
But the 60° bushings are mfg to a much higher tolerance than the commercial ones.