Bagels are sometimes vegan but not always.
It depends on where you're buying them and whether or not the baker uses eggs and other animal products in their bagel recipe.
You always want to read the ingredients or ask the baker about the bagels you're buying.
Ingredients to look out for are: eggs, honey, l-cysteine, and milk.
The common brand of bagels Thomas' has many accidentally vegan options including bagel thins and mini bagels.
Many grocery store brand bagels are also accidentally vegan. Always read ingredients!