Zone 5 - Northern IL

I just built a 2x8 slightly raised bed on the SW side of my yard. I plan to plant 1 Caroline, 1 Anne, and 1 Royalty bare root plants this spring. I figure those 3 should fill the box up plenty soon enough.

I made it so I can mow all around the box. It is only a couple feet from my neighbors yard, but his is just lawn, no beds. It is also right next to our utility box and lines. My biggest fear is that I will not be able to contain the suckers. My neighbor mows his yard twice as often as I do, so will us mowing around this keep the raspberries contained? There is no way I could dig much outside of the box if they escaped. Just mowing is my option.

So my question is, is this a good set up or am I going to be ticking my neighbor off? Is mowing a yard adequate to control the suckers?? I figured the slightly raised box would give me a defined boundary to keep them in. I am probably putting way too much thought in to this as it is keeping me up at night worrying about it!

Thank you for any help :)