I was thinking of Wesley Clover too, that would be my recommendation. Going further west towards Fitzroy park will just be a lot more travel time to get anywhere in Ottawa. Wesley park is right off the 417, easy access to park, then right back onto the highway no matter which way you are heading (to or from). Heading out Fitzroy is all little 2 lane roads, especially getting to the park. I am not sure if Wesley park can accommodate the BH, but I would venture that they would be able to with no problems.
I have never been there though, as those are my old stomping grounds. I never brought the TT there as I had a house to go to whenever I decided to head east.
Highly recommend the War Museum in Ottawa while you are there, not sure how familiar you are with the Nations Capital and what there is to offer. I was just there at the museum over Christmas and was amazed at all of the items in there, last time I was in the museum it was all the way down town and MUCH smaller.