There are actually three ways in which you can treat the $\bot$ (and same for $\top$, if that is part of your language).
As an atomic formula (different though as it is from the more 'typical' atomic formula that has a predicate term)
As something that is not an atomic formula but still 'acts like' an atomic formula in its uses. For example, one could define the set of 'base formulas' as the set of 'atomic formulas' (the ones involving predicate symbols) together with $\bot$ (and $\top$), and those 'base formulas' can be combines with others using truth-functional connectives.
As a syntactical shorthand for a generalized disjunction with $0$ disjuncts. That is, you can see the $\bot$ as neither an atomic formula nor acts like it, but rather as a complex formula (namely, a generalized disjunction (that disjuncts together any number of statements) ... with $0$ disjuncts!). This might be helpful when you have generalized disjunctions as part of your formal way of building up statements (as opposed to more 'traditional' approaches where disjunctions are typically understood as taking exactly two statements for its disjuncts), and when you do that, it could also be useful (e.g for your meta-theoretical proofs) to allow generalized disjunctions to have $0$ disjuncts ... and use $\bot$ as a way of expressing those.
Oh, and there is actually another use I sometimes see for the $\bot$, which is to use it as the truth-value $False$, or as the value $0$ in a boolean algebra. I really don't like that practice, as there is a big important difference between a truth-value and a statement (even if it is one, like the $\bot$ that always takes on a certain truth-value), so in my eyes it is not deserving of a 4. ... but like I said, you may see this in other books yet.
From my experience, I would say 3 is rather unusual, but both 1 and 2 are fairly common.