Interestingly, The Wesleyan Church can be attractive to Baptists and Pentecostals for a number of reasons. To Baptists, it offers a very familiar low church feel with a more robust connecting network. All they have to do is deny eternal security or not bring it up. ;-) For Pentecostals, it's very similar except tongues aren't generally allowed in worship. But then again, a lot of charismatic churches don't speak much tongues in worship either.
So what do Wesleyans believe about baptism? Here's the official statement:
"We believe that water baptism and the Lord's Supper are the sacraments of the church commanded by Christ and ordained as a means of grace when received through faith. They are tokens of our profession of Christian faith and signs of God's gracious ministry toward us. By them, He works within us to quicken, strengthen and confirm our faith.
"We believe that water baptism is a sacrament of the church, commanded by our Lord and administered to believers. It is a symbol of the new covenant of grace and signifies acceptance of the benefits of the atonement of Jesus Christ. By means of this sacrament, believers declare their faith in Jesus Christ as Savior."
But official statements often don't really tell the whole story. Here's the skinny:
"Until recently, baptism has not been much of an emphasis of the Wesleyan Church. Most churches practice believer's baptism and have done it maybe once a year. You may find traces of individuals who have never been baptized or who were baptized as infants, but these are rare. Few if any would have any theology of baptismal regeneration and in practice, our sense of baptism as a sacrament has generally been somewhat weak."
Now the background:
1. One of the main predecessor churches of the Wesleyan Church (Pilgrims) had significant Quaker elements. So many of the early Pilgrims were like the Quakers or Salvation Army. They not only did not emphasize baptism. Many of them were not baptized at all. My grandfather only got baptized because he was asked to perform a baptism. He didn't think he should perform a baptism if he wasn't baptized himself.
By far the majority of Wesleyans would now say that, even though baptism does not actually save you, it is a central practice of the historic church with sacramental power. Nevertheless, we still would not believe that a person has to be baptized in order to be saved.
2. The other main predecessor church (Wesleyan Methodist) withdrew directly from the Methodist church over abolition. Accordingly, it retained the possibility of infant baptism. Again, the idea is not that such a baptism saves the child or ensures that the child will eventually be saved.
By far the majority of Wesleyans now practice believer's baptism, so much so that many would be surprised to know that it is still allowed to practice infant baptism in the Wesleyan Church. Nevertheless, my wife and I preferred for our children to be reckoned "in" the church and to have to leave it rather than to reckon them "out" until we could persuade them to come in. Dr. Bud Bence accordingly baptized our children in a Wesleyan Church.
So basically, in practice we have moved toward the Baptists, although in our theology, we neither specify the method (immersion, sprinkling, or pouring) nor the timing (believer's or infant). For Wesleyans, baptism is a sacrament in which every believer should participate, but it is neither essential for salvation nor something whose particulars we should fight about.
Were you baptized as an infant? You do not need to be re-baptized. If it would be significant for your spiritual pilgrimage, though, we will not stop you. Were you never baptized? You should very, very seriously consider it, although we will still call you a brother or sister if you choose not to.