What sort of traffic is going to use the walkway?
Feet? Wheels? Crutches? Walkers?

just my own two feet. i could keep it as grass but i just dont see the point of watering, fertilizing, and mowing a 2-3 ft strip. this is basically an access path for me to walk along and kneel on when i need to weed or prune my shrubs and flowers. it will be in my front yard which receives virtually no traffic since we all spend our outdoor time in the fenced-in backyard. theres also two mulberry trees in my front yard which in 2 years will be much larger. since they drop berries and leaves once a year, my idea of pea gravel might not be a good one when its time to clean up. so i'm thinking large pavers now which i can sweep clean, but i still need a substrate between the pavers besides having to pour concrete. i guess im hoping theres a more effective solution to using landscape fabric (bermuda grass just laughs at that stuff). anyone have a better idea?

Ugh! I do hate bermuda....... this is the one thing I use chemicals on. It's the only thing Ive found that works, but even with Roundup you have to spray every couple weeks for about two years if it is really established. First I would dig out as much as you can and throw away all the pieces of roots and leaves. Then do the spraying. The problem with plastic and rocks is that the roots are really strong and will break thru your barrier.... sorry I cant be more encouraging.

What you describe will NOT keep out the bermuda.

You need solid concrete.

Bermuda will even grow right over solid concrete unless you keep it trimmed back.

The best way is to keep fighting all the bermuda that gets into your yard.