Some gardeners have had success with placing chicken wire around the base of the rose as squirrels don't like to go over the wire or dig in it.

Go to your local beauty salon and gather some human hair. Sprinkle the hair in and around you pots. This works very well with rabbits too.

New to roses old to gardening.

I'm also new to roses but old to (container) gardening

I'm also new to roses but old to container (roof-top) gardening. I've found that sprinkling a pungent spice such as cumin, curry, or hot pepper flakes on the soil and even dusting the leaves with powdered spice can often keep squirrels, cats and bugs out of the container. Your yard or rooftop smells (temporarily) like an Indian restaurant, but the critters don't seem to like it. I've never tried this on my 2-day old rose bushes, but it sure works on sunflowers (which squirrels love).

Depends on density of the squirrels' population. In the city for me works only mechanical protection - wire mesh on the top of containers, for bushy ones - rose collar (green dense plastic mesh) around the top of container and bottom of the plant, bamboo skewers sharp point up work too, but look very ugly. If other soil sources around are difficult to dig, squirrels turn to easy to dig soils.