Yes, you can have bread on a low-fat diet, just be careful what type, read labels, or bake your own where you can control the ingredients.
As with any food, bread sneaks up on you if you don't watch how much you're eating.
Did you know most fresh bread bakeries will slice your bread thinner if you request it? That cuts down on calories and fat but lets you have a top and bottom slice on that sandwich. You'd also be surprised at how wonderfully it toasts up when cut thinner!
When preparing any recipe, look at the ingredients and consider if any lower-fat or lower-calorie substitutions can be made.
Try new spices. Try new vegetables and fruits. Try new prep methods. And, above all, try new recipes. Dieting is a time to liven up your meals, not fall into a boring routine that leaves you munching chips to make your tastebuds happy.