What is the SBC's stance on what/how salvation is/works? What is the Southern Baptist Convention's stance on what salvation is and how it works? 

Is there an official doctrine? 

Is it challenged by prominent members?
Straight from the source, at http://www.sbc.net/bfm/bfm2000.asp#iv
This is challenged by followers of liberal theology, who deride the leaders of the SBC as fundamentalists.

Salvation involves the redemption of the whole man, and is offered freely to all who accept Jesus Christ as Lord and Saviour, who by His own blood obtained eternal redemption for the believer. In its broadest sense salvation includes regeneration, justification, sanctification, and glorification. There is no salvation apart from personal faith in Jesus Christ as Lord.
A. Regeneration, or the new birth, is a work of God's grace whereby believers become new creatures in Christ Jesus. It is a change of heart wrought by the Holy Spirit through conviction of sin, to which the sinner responds in repentance toward God and faith in the Lord Jesus Christ. Repentance and faith are inseparable experiences of grace.
Repentance is a genuine turning from sin toward God. Faith is the acceptance of Jesus Christ and commitment of the entire personality to Him as Lord and Saviour.
B. Justification is God's gracious and full acquittal upon principles of His righteousness of all sinners who repent and believe in Christ. Justification brings the believer unto a relationship of peace and favor with God.
C. Sanctification is the experience, beginning in regeneration, by which the believer is set apart to God's purposes, and is enabled to progress toward moral and spiritual maturity through the presence and power of the Holy Spirit dwelling in him. Growth in grace should continue throughout the regenerate person's life.
D. Glorification is the culmination of salvation and is the final blessed and abiding state of the redeemed.