There are many ways to go about it, but a straight-forward one is to use Django's connection object:
from django.db import connection
This creates a direct connection to your database. With this, you can either execute direct SQL queries:
cursor = connection.cursor()
bbox = (97.82, 30.25, -97.65, 30.29)
cursor.execute("SELECT * FROM myTable WHERE ST_MakeEnvelope(%s, %s, %s, %s, 4326) && ST_Transform(myTable.geom, 4326)", bbox)
result = cursor.fetchall()
Or you can pass your query to a function using Postgres' plpgsql (calling it, say, fn_grab_polys_bbox), and execute it:
cursor = connection.cursor()
bbox = (97.82, 30.25, -97.65, 30.29)
cursor.callproc('fn_grab_polys_bbox', bbox)
result = cursor.fetchall()
Django's connection object is actually referencing Python's own DB-API, which works with a variety of databases. Hence, if you need to call a function, or a table, from a different database than the one you set for your project, you can even do a specific connection to that and repeat the above steps, the returned objects will be the same.