Agents can create rich representations, yet these representations are rarely used as a medium for expressing user intent. We present **Agent-Bound UI**, an interaction model that separates reusable interaction structures from task-specific meanings. Agents bind task-specific meanings to interactions in reusable views and publish the resulting bindings as shared state, enabling humans and agents to understand and act on shared surfaces whose meanings vary across tasks. We implement ABRA, a framework-agnostic prototype of Agent-Bound UI, in which users and agents collaborate through chat and shared interactive canvases. We demonstrate ABRA through a representative use case and evaluate four LLM-backed agents on canvas authoring, owner-side consequence resolution, and cross-agent invocation. The code and demo video are available at https://github.com/megagonlabs/abra.