I would glue-baste it. In my opinion, the bias works in your favor on this project. My technique is to put a pin at the quarter-inch mark (where you want to stitch) of the top piece, then through to the quarter-inch mark of the bottom piece. Put a dot of glue in the seam allowance at this spot, touch with a hot iron to dry, and glue the 2 pieces together, then remove the pin. Repeat at the other end of the piece you are sewing. Then, without touching or pinning anywhere else, hover the iron and steam the length of the item you're sewing. The steam will help the bias fabric relax and ease in any excess. At this point you can stitch, or if the piece is really long and you'd feel more comfortable pinning, then add a few more dots of glue in the seam allowances. Once the seam is stitched and you're satisfied, slide an awl between the fabrics in the seam allowance to un-glue the glue dots.
Also, spinning your seams will help a lot with the bulk where intersections meet.