How you print B&W will depend on your software and printer. One of the difficulties is ensuring what you see on the screen is printed accurately, especially the shadows and the highlights. Using a correctly profiles system can help, but also knowing at what point the highlights blow out and the shadows will block up is useful.
For example if you have a highlight with a value of say 240 ( R,G,B) will this print as a density or will the printing system simply show this as white. Same happens with shadows, at what point do you start to see differentiation in tones at the shadow end. So if you printer effectively prints everything a black with no differentiation from say 0-20, there is no point in trying to hold detail in the image that has a value of 10.
I normally print B&W out of Lightroom which uses percentages rather than 0-255 values. I find that I can hold highlight detail up to about 95% after that it gets problematical. Shadows anything lower than 10% are really too solid to show detail usually. This is on a profiled Epson 2880. Other printers it may be different. Relating these numbers back to a convention 0-255 system I would guess that the highlights are constrained to about 245-240 with the shadows to around 25, but that's just a guess.
Really the only way to see if the image can be printed satisfactorily is to try it and see, and make an assessment as a result of the test. But as a guide keep the highlights to below 235 and the shadows above 30