There has been a concerted effort by the neuroimaging community to establish standards for computational methods for data analysis that promote reproducibility and portability. In particular, the Brain Imaging Data Structure (BIDS) specifies a standard for storing imaging data, and the related BIDS App methodology provides a standard for implementing containerized processing environments that include all necessary dependencies to process BIDS datasets using image processing workflows. We present the BrainSuite BIDS App, which encapsulates the core MRI processing functionality of BrainSuite within the BIDS App framework. Specifically, the BrainSuite BIDS App implements a participant-level workflow comprising three pipelines and a corresponding set of group-level analysis workflows for processing the participant-level outputs. The Anatomical Pipeline extracts cortical surface models from a T1-weighted (T1w) MRI. It then performs surface-constrained volumetric registration to align the T1w MRI to a labeled anatomical atlas, which is used to delineate anatomical regions of interest in the MRI brain volume and on the cortical surface models. The Diffusion Pipeline processes diffusion-weighted imaging (DWI) data, with steps that include coregistering the DWI data to the T1w scan, correcting for susceptibility-induced geometric image distortion, and fitting diffusion models to the DWI data. The Functional Pipeline performs fMRI processing using a combination of FSL, AFNI, and BrainSuite tools. It coregisters the fMRI data to the T1w image, then transforms the data to the anatomical atlas space and to the Human Connectome Project's grayordinate space. The outputs of each pipeline can then be processed during group-level analysis. The outputs of the Anatomical Pipeline and the Diffusion Pipeline are analyzed using the BrainSuite Statistics Toolbox in R (bstr), which provides functionality for hypothesis testing and statistical modeling. The outputs of the Functional Pipeline can be analyzed using atlas-based or atlas-free statistical methods during group-level processing. These analyses include the application of BrainSync, which synchronizes the time-series data temporally and enables comparison of resting-state or task-based fMRI data across scans. We also present the BrainSuite Dashboard quality control system, which provides a browser-based interface for reviewing the outputs of individual modules of the participant-level pipelines across a study in real-time as they are generated. BrainSuite Dashboard facilitates rapid review of intermediate results, enabling users to identify processing errors and make adjustments to processing parameters if necessary. The comprehensive functionality included in the BrainSuite BIDS App provides a mechanism for rapidly deploying the BrainSuite workflows into new environments to perform large-scale studies. We demonstrate the capabilities of the BrainSuite BIDS App using structural, diffusion, and functional MRI data from the Amsterdam Open MRI Collection's Population Imaging of Psychology dataset.