As long as the bagels are made without hen eggs or any bovine-related dairy products, they are considered to be vegan. In most recipes, bagels only contain yeast, flour, salt, water and food for the yeast, which can be malt powder, malt syrup or sugar.
Many baked goods are vegan in nature. The only ones that are often not are cakes because they usually require the use of eggs, milk and sometimes even butter, and certain sweet breads, which often contain one of those three ingredients. However, nearly all forms of bread, such as sandwich bread, rolls, buns and English muffins, are safe for vegans to eat.