There are good invitations, but if you want to see multiplication, there might be better ones:
It's unusual for someone to say, "How can I become a Christian?" They are much more likely to respond to a specific suggestion from you. Hopefully you've made clear the cost of following Jesus when you shared to good news with them. You could say, "Would you like to invite Jesus into your life," but it might be better to ask, "Are you ready to surrender your life to Jesus?" The one might lead to a decision, the other to a disciple.
Then teach the new disciple how to share his/her story with his friends and family, inviting them to become Jesus followers too.
Do you ask the new believer to come with you to church?
There might be a better way. How about, "Do you have any friends who might be interested in learning more about Jesus too? Could we get together with them?"
If you invite someone to come to church with you, whether legacy or house church, you may miss out on the opportunity to reach their oikos, or circle of influence. The slow way to multiply is to add people to your group until it is big enough to multiply into two. The faster way is to start with an existing community and watch them become a church as a group together. So better to meet with the new disciple's existing circle of influence within their familiar environment.
Suggested activity: Would the people in your church know how to pray with someone to become a Christian? Have them practice this skill with each other.