The best book-length biography of Catherine Booth remains F. Booth-Tucker, The Life of Catherine Booth, the Mother of the Salvation Army (1892). Several histories of Salvationism are valuable in gleaning details of her life and influence; see particularly the six volume History of the Salvation Army by R. Sandall and others (1979) and Pamela J. Walker, Pulling the devil’s kingdom down: the Salvation Army in Victorian Britain (2001).
A critical study of Catherine’s commitment to preaching is available: Pamela J. Walker, ‘A chaste and fervid eloquence: Catherine Booth and the ministry of women in the Salvation Army’ in Women preachers and prophets through two millennia of Christianity, (ed. B. M. Kienzle and P. J. Walker, 1998). Walker also contributed her DNB entry, which is useful.
At a more popular level, Christian History vol. 26 (1990) was devoted to William and Catherine Booth, and contained some quotations from her writings.
Her defence of female preaching was occasioned by a published attack on Phoebe Palmer’s preaching ministry; the argument is striking in that most defences of the day relied (as John Wesley had done) on some account of an ‘extraordinary call’: the Holy Spirit may, at times, suspend the normal order of things and elevate a woman to the pulpit. Catherine Booth’s account was different: female subjection was an evil occasioned by the Fall, and corrected by Christ’s work of redemption; women and men are indifferently called to preaching ministry in the New Testament dispensation, and this is evident in the NT itself; the texts usually cited to forbid the pulpit to women are either being misread or misapplied, or they are local and occasional instructions, which should not be regarded as binding on the life of the church forevermore. She drew extensively on the best nonconformist scholarship of her day to make the argument.