Try modeling the bridge table as a fact (factless fact table) or in olap terms, model a cube with source as bridge table with addl column defined with constant value (=1) perhaps. Maybe you can use AWM mapping and key in the constant in awm mapping screen (instead of dragging a column from bridge table to map to measure).
Define additional olap measures (calculated measures) like sum, max, count of dim1 or count of dim2 or count of dim1/dim2 combination etc. as needed for analysis.
For text measures/attributes, you can attempt concatenating the strings into a long delimited list of values and convert many codes into a single display string.