Exploring alternative ideas by rewriting text is integral to the writing process. State-of-the-art Large Language Models (LLMs) can simplify writing variation generation. However, current interfaces pose challenges for simultaneous consideration of multiple variations: creating new variations without overwriting text can be difficult, and pasting them sequentially can clutter documents, increasing workload and disrupting writers' flow. To tackle this, we present ABScribe, an interface that supports rapid, yet visually structured, exploration and organization of writing variations in human-AI co-writing tasks. With ABScribe, users can swiftly modify variations using LLM prompts, which are auto-converted into reusable buttons. Variations are stored adjacently within text fields for rapid in-place comparisons using mouse-over interactions on a popup toolbar. Our user study with 12 writers shows that ABScribe significantly reduces task workload (d = 1.20, p < 0.001), enhances user perceptions of the revision process (d = 2.41, p < 0.001) compared to a popular baseline workflow, and provides insights into how writers explore variations using LLMs.