I need to write a paper regarding the Colonial Period on one author. I like Anne Bradstreet's writings, but I am having difficulty coming up with a thesis. What is a good thesis or beginning to discuss this period and this author? It cannot be a biography; it has to be of her writing.

I am assuming your paper must analyze Bradstreet’s writings within the context of the colonial time period.
Bradstreet was the first English Colonial writer to be published, a feat she achieved because of her prolific writing habits. Within her poetry, Bradstreet often wrote about her feelings of homesickness for Old England in her New England life. This tension between the old way of life in the motherland and the new way of life in the American colonies captures the experience of many of the first colonists to arrive, who found that there were many adjustments to be made in their new home.
Furthermore, Bradstreet’s poetry reflected her role as a Puritan wife, giving the modern reader a glimpse into women's roles in the Colonial Era. Bradstreet often addresses the gender expectations of Puritan society within her poems, often criticizing the belief that women’s voices were not deemed worthy of inclusion in public discourse. She chafed against the restrictions placed on her by boldly asserting women’s worthiness, questioning her faith, and declaring her passionate love for her husband.
Although Bradstreet never intended to publish her writings, her body of work reflects the complex imagination of a Puritan woman who was both an upstanding member of her society and an individual with a rich internal life that often scrutinized Colonial society.
Hopefully, this discussion will help you with a thesis. You may choose to focus on how her writing centers on gender roles/expectations, religion, or society. Each of these thematic ideas can be examined in a number of her poems so that you could write an entire paper focused on one.