I think every IBS-D or A has had that problem at one point! I know Jenny runs but has to do the first few miles in a section of the park with toilets! I've had to go in the woods before when out walking.
Okay, the urgency should ease as you stick to the diet...a SFS will also help. Acacia seems to be very good for IBS-A, probably b/c it's gentle but effective (possibly b/c it's so gentle you can take loads of it! ).
In the meantime, if you are going through a D stage, then Immodium taken as a preventative (works best when taken daily) will slow your GI system down. That's how Immodium works which is why it's great for urgency as well as full-on D.
Finding a walking route or a park with plenty of accessible toilets is a good idea! Or try walking faster, even power-walking...that would get you to and from the shops quicker as well as burning more calories.
And you can get great exercise CDs/videos for at home. As you're above your landlord (no jumping I guess?) I'd suggest yoga. Om: Yoga in a Box Beginner level has been great for me.
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No problemo!
I've had to go in the woods before when out walking. 
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