Convert to Bubble Letters
Retina, 20 bytes

T`Lld`Ⓐ-⓪①-⑨


Try it online!

How it works

There's a gap between the code points of (0) and (1), but &ndash; fortunately &ndash; the character right after (z) is (0). This way, we can transliterate the character from concatenated ranges A-Za-z0-9 to the characters of the concatenated ranges (A)-(0)(1)-(9).

The rest is straightforward: T activates transliteration mode, Lld yields all uppercase ASCII letters (L), all lowercase ASCII letters (l) and all digits (d), and Ⓐ-⓪①-⑨ the corresponding bubble characters.