It is important to look at context. To whom do the Spirit and the bride say, "Come?"
“16 “I, Jesus, have sent My angel to testify to you these things in the churches. I am the Root and the Offspring of David, the Bright and Morning Star.” 17 And the Spirit and the bride say, “Come!” And let him who hears say, “Come!” And let him who thirsts come. Whoever desires, let him take the water of life freely.” (Re 22:16-17 NKJV)
So the context is that the Spirit and the bride (Christ's church) are saying, "Come" to Christ. As John Gill wrote in his commentary: "Hearing Christ say that he should come quickly, Re 22:7,12 the Spirit and the bride express an earnest wish, and a most affectionate desire after his coming: by "the Spirit" may be meant the Spirit of God in the hearts of his people, who not only convinces them of, and acquaints with the coming of Christ to judgment, and gives them reason to expect it, but fills their souls with the love of his appearance, so that they look and long for it, and hasten in the breathings of their souls after it."
This view is confirmed later in the chapter:
“He who testifies to these things says, “Surely I am coming quickly.” Amen. Even so, come, Lord Jesus!” (Re 22:20 NKJV)