Biobased substitutes for plastics are a future necessity. However, the design of substitute materials with similar or improved properties is a known challenge. Here we show an example case of optimizing the mechanical properties of a fully biobased methylcellulose-fiber composite material. We tackle the process-structure-property paradigm using Bayesian optimization with Gaussian process regression to map the processed material composition to the final mechanical properties of new bio-based solid foams. We exploited the fast-to-measure rheological properties of the liquid biofiber suspensions processed into foams to show how these collapse to an auxiliary sub-space of low dimensionality for design. The optimal compositions for methylcellulose-fiber foams shown here correspond to two distinct cases: high methylcellulose content for the formation of strong closed-cell foams, and high fiber contents with approximately equal amounts of methylcellulose for the formation of methylcellulose-bound fiber networks. The novel approach is transferable to other biobased foam compositions with different fibers and additives. This new approach allows the rational design of bio-based plastics replacements by encompassing desired final material properties, descriptors of materials processed, and knowledge of the process.