Edit I thought amssymb provides \cupdot which does what you want... but it doesn't.
\usepackage{MnSymbol} provides \cupdot and \bigcupdot but is incompatible with amssymb which is unfortunate.
Sometimes disjoint union is depicted using \sqcup which has the advantage of being in amssymb
What's this union symbol doing without anything on its left?
[University] Set Theory - Union and Intersection
How do you remember set theory basic symbols?
Why is the set intersection symbol an upside down "U" is it random or is there a reason
What is the symbol for union of sets?
What is union of sets with examples?
What does union mean in math sets?
Videos
Edit I thought amssymb provides \cupdot which does what you want... but it doesn't.
\usepackage{MnSymbol} provides \cupdot and \bigcupdot but is incompatible with amssymb which is unfortunate.
Sometimes disjoint union is depicted using \sqcup which has the advantage of being in amssymb
Another possibility to go around the problem that there is no such symbol in amssymb is to use the dot-accent: \dot{\bigcup} or also \dot\bigcup. This works for all symbols, and might very well be the reason that there are no dotted symbols in amssymb.
To let TeX treat such a new construct as an operator in terms of spacing though, you need to use \mathop and \mathbin, that's to say \mathop{\dot{\bigcup}} and \mathbin{\dot{\cup}}.