Generative AI offers new resources for collaborative design ideation, yet how designers work with it as a shared concept develops remains underexplored. We developed DuoSketch, integrating a shared canvas and live transcripts with a separate AI for each member of a pair. An exploratory qualitative study with 12 pairs identified three challenges: unresolved fit between AI proposals and shared design purposes, shared meanings not expressed in AI responses, and agreed changes missing from later outputs. We found that pairs navigated these challenges through bridging work in two directions: AI -> Shared Design (reworking features, developing uses, and assessing fit with shared requirements) and Shared Design -> AI (supplying materials, explaining meanings, and communicating decisions). We discuss how future AI systems can support the joint exploration and articulation of design ideas.

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