HE HE HE...INDOOR cycling...Now why didn't *I* suggest that one. LOL

Some thoughts on that...

If you have a bike, you can get a rear wheel straining stand. That is a stand where you lock the rear axle to the the device and let the rear wheel sit on a roller that provides resistance. Any good bike shop can help you on that one. Also, regardless of whether you use a training stand or an indoor cycle machine get a fan. That will help you keep cooler. You will want to have your cycle on a cloth to avoid sweat on any surfaces you can't easily clean. Make sure the bike is properly fit for you. This will have a huge impact on avoiding unneeded stress on joints. Again, a good bike shop can help in this department.

BTW, in spite of my "militant" position about protecting yourself from dogs, I understand that kind of fear and certainly don't want you to step out of your comfort factor.