Recent data search platforms use ML task-based utility measures rather than metadata-based keywords, to search large dataset corpora. Requesters submit a training dataset and these platforms search for augmentations (join or union compatible datasets) that, when used to augment the requester's dataset, most improve model (e.g., linear regression) performance. Although effective, providers that manage personally identifiable data demand differential privacy (DP) guarantees before granting these platforms data access. Unfortunately, making data search differentially private is nontrivial, as a single search can involve training and evaluating datasets hundreds or thousands of times, quickly depleting privacy budgets. We present Saibot, a differentially private data search platform that employs Factorized Privacy Mechanism (FPM), a novel DP mechanism, to calculate sufficient semi-ring statistics for ML over different combinations of datasets. These statistics are privatized once, and can be freely reused for the search. This allows Saibot to scale to arbitrary numbers of datasets and requests, while minimizing the amount that DP noise affects search results. We optimize the sensitivity of FPM for common augmentation operations, and analyze its properties with respect to linear regression. Specifically, we develop an unbiased estimator for many-to-many joins, prove its bounds, and develop an optimization to redistribute DP noise to minimize the impact on the model. Our evaluation on a real-world dataset corpus of 329 datasets demonstrates that Saibot can return augmentations that achieve model accuracy within 50 to 90% of non-private search, while the leading alternative DP mechanisms (TPM, APM, shuffling) are several orders of magnitude worse.