Concrete Hardiiboard might be a better barrier related to lasting in the moister in the ground.

1. Is it normal for a rose root to travel that far? OR! Do you have moisture that is attracting the roots?
2. Do you think the neighbor would share some opinions and help just incase some roses have problems?
3. How deep do you feel or know the roots are traveling? A sharpshooter shovel should cut roots and part ground for Hardieboard.

I Know The Feeling! My neighbor and I tried to keep my St Augustine grass from traveling into his Bermuda. Where I poured a 6X6â concrete border (with two 3/8â rebar strings) under the back yardâÂÂs fence it worked vs where he used locking border stones as deep.

Good Luck!

On the whole, most roses don't send roots down very deeply so they're usually easy to cut off with any shovel that has a wide/sharp enough blade to plunge directly downward into the soil to a depth of perhaps 12"-14".
Before removing the shovel, rock it back and forth towards and away from you leaving a "V" shaped hole. After you've created your trench, use a filler of some sort to create your root barrier... almost anything will work such as a piece of plywood, galvanized metal gutter material (watch for sharp edges), roof shingles, or whatever material you may have on hand or be able to round up. Fill in both sides of the trench and you're good to go.
On the other hand, cut off the roots near the fence line at the start of your growing season and you probably won't have to do it again until the start of next season.
Good luck.
Steve

Steve, Is That Tyler, TX Good Rose Experience?

Thanks for the help everyone. When I looked at the roots today they actually were very close to the surface of the ground, which surprised me (not being the rose expert that I am!)

I think the rose bushes love my soil because I put all sorts of good compost in it and water regularly. And the plants closest to the rose bushes always have stunted growth, poor things. So I will probably try to fill the trench with plywood or something.

Thanks for your help everyone! Any other ideas, feel free to share, I'll still be reading this.

Loger, no Tyler experience here... just a lot of years growing roses in limited spaces ;o)

As to the stunted growth idea, the roses may be stealing a bit of your moisture and nutrients but off hand, I imagine that growing close to a fence with its associated shade except during the noon hours in growing season may have more to do with the stunting than the rose roots do. Too, the edges of any garden invariably get less moisture and nutrients than the more centered areas do just by the very nature of layout.
Although you don't say how big your plot is or in what direction it's oriented (east, west, etc.), it may be as easy as planning your plantings so that the varieties that need the most sun/lighting hours are closer to the center or sunniest spot in your plot while varieties that can take more shade hours are situated appropriately. Sometimes, it's the little things that allow the most usage of available space such as you have and not necessarily the plants you've chosen. A little pre-planting research will help with those issues before planting time rolls around again.
Good luck!
Steve