John 6:44 "No one can come to me unless the Father who sent me draws him, and I will raise him up at the last day." - I think this is the scripture you are referring to
Revelation 22:17 The Spirit and the bride say, "Come!" And let him who hears say, "Come!" Whoever is thirsty, let him come; and whoever wishes, let him take the free gift of the water of life.
The Spirit is sent from the Father
John 14:16-17 "If you love me, you will obey what I command. And I will ask the Father, and he will give you another Counselor to be will you forever - the Spirit of truth.
The Bride is one with Jesus
1 Corinthians 6:16-17 Do you not know that he who unites himself with a prostitute is one with her in body? For it is said, "The two will become one flesh." But he who unites himself with the Lord is one with him in spirit.
Okay, the Spirit comes from the Father who gives it to you. The bride are those people who are already united to Christ spiritually, so the both of those working in tandem are another route the Father draws people to the free gift of the water of life. Am I making sense?