Border or not
 

I just measured my 3D bowtie quilt & my perfect backing my backing is 54 inches wide & my quilt (without borders) is about 51 inches. The quilt is ready for borders. With the borders my backing will too narrow. Can I leave off borders or would that look too unfinished.

I only use borders once in a while. Your quilt, your rules.

I generally prefer borders on my quilts. But if you decide not to add borders, you are cutting it very close with only 3" to spare. I would be tempted to add a strip of another fabric in there to make it a bit wider. I almost always do decorative backs. I love the look of them. :)

Hard to say without a picture. If you like it the way it is, then don't add borders. It is personal choice, after all.
If you want to add a border, you could always make a row of bow-tie blocks and inset them in the perfect batting. Adding back art is all the rage. With 3" of play, you'll need to be careful when you sandwich so you don't run off.

I am a border person, I think that it frames the quilt. That being said, don't let the quilt police stop you from doing what you like.

If it is only because you are not having enough backing, you might regret not doing the extra work of adding to the backing. I have been known to take things apart because i was not satisfied with the outcome.

Borders are for you to decide. Some quilts need enlarging and borders required. Some people just like the look of borders ( one or more) . Others like the piecing to go to the edge without a border just binding.Others like to birth the quilt I've rightsides together and machine almost ( 6"- 10" gap) round and pull through gap to rightside.

the choice is yours you will get numerous advice but at the end it is your quilt.

You can do whatever you want to do. Not all quilts have borders.

It's totally up to you. If you Are thinking about leaving them off, you can still frame the quilt using a strongly contrasting binding.

Whether you use a border or not should be decided by the finished design you desire on your quilt not on the width of a piece of backing fabric. A piece of fabric 54 inches seems like something other than quilting cotton-which can be fine. However, you can certainly add to the back by cutting vertically or horizontally at some pleasing dimension and inserting a strip of another color, something you used on the quilt surface or unused blocks, etc. Just don't let the dimension of the back be the dictator or your quilt.

Will the quilt as is work well with what you had planned? You don't need to add the borders. I do mostly quilts without borders.