Multiple speech biomarkers have been shown to carry useful information regarding Amyotrophic Lateral Sclerosis (ALS) pathology. We propose a two-step framework to compute optimal linear combinations (indexes) of these biomarkers that are more discriminative and noise-robust than the individual markers, which is important for clinical care and pharmaceutical trial applications. First, we use a hierarchical clustering based method to select representative speech metrics from a dataset comprising 143 people with ALS and 135 age- and sex-matched healthy controls. Second, we analyze three methods of index computation that optimize linear discriminability, Youden Index, and sparsity of logistic regression model weights, respectively, and evaluate their performance with 5-fold cross validation. We find that the proposed indexes are generally more discriminative of bulbar vs non-bulbar onset in ALS than their individual component metrics as well as an equally-weighted baseline.