Ask Mr. Smarty Plants

First of all, our focus and expertise are with plants native to North America (excluding Mexico) so we can't really help you with non-native plants.  Bougainvillea, for instance, is native to South America.  I'm not sure which which trumpet vine you mean—the North American native Campsis radicans (trumpet vine), or Distictis buccinatoria (blood-red trumpet vine), a native of Mexico and Central and South America.  You can search on the internet for growing conditions for the two non-native species; but, Campsis radicans (trumpet vine) is not evergreen, won't do well in shade or part shade, and although it is native to North America, is not native to southern California.

There is one evergreen vine (with two varieties) that will grow in sun to part shade and is native to your area.  These two varieties are:

Lonicera subspicata var. denudata (chaparral honeysuckle) and here are more photos.

Lonicera subspicata var. subspicata (Santa Barbara honeysuckle) and here are photos. 

There is another honeysuckle, Lonicera hispidula (pink honeysuckle), native to your area that is semi-evergreen and will grow in the shade.

Finally, here are three vines that are not evergreen but will grow in part shade or shade and would be a beautiful vine on your trellis.

Clematis lasiantha (pipestem clematis) will grow in sun and part shade but is winter deciduous. Here is more information.

Clematis ligusticifolia (western white clematis) will grow in sun, part shade and shade, is deciduous, and needs moisture in summer.  Here is more information.

Clematis pauciflora (ropevine) grows in part shade and does well in dry, hot areas.  Here are photos.

Here are a photos of a few of the above plants from our Image Gallery:

Lonicera hispidula

Clematis lasiantha

Clematis ligusticifolia