All the principles of design that you already know apply equally to monochrome as they do to multi-colored work. Working with a single ink (whether it's black or any other color) may feel unfamiliar, but it is not fundamentally different. I suspect that it is unfamiliarity that is making you uncomfortable, not any lack of skill.
A good design will always work in monochrome ("black and white"). If it doesn't, then there is probably something fundamental wrong with it. As in photography, color can "blind" you to flaws in the work that become visible when the color is removed. Pull a few color images into Photoshop and practice making black and white versions that work well.
There are no different design principles for monochrome. You apply the same rules, but use shades and tints of your single color to emphasize, contrast, lead the eye and balance a composition, just as you would with color. If you look around at magazines, posters, or on the web you will find many examples of good monochrome design.
Here's what I would suggest: build your design using any colors you like, then create a grayscale version. You will find that you must adjust the relative values of your gray tints to achieve the effect of the color version, and you may have to adjust weight of some elements for the best impact, but you will still be able to achieve an effective design.
It may be that the budget will allow an ink other than simple black, provided it is just one ink. If that is the case, a suitable Pantone color will allow you to create "color" using different percentages of screen, just as you would in grayscale.
I'm offering this as a way to ease you into designing in monochrome, but you will find it both good discipline and an excellent way to improve your technique to create a few designs in monochrome then color them.