Yes, there are public washrooms in a few locations:
Cochrane Information Centre (CIC) at The Station at Cochrane Crossing, 360 Railway St W. The CIC is open daily, 8:30am-4:30pm
There are also washrooms open daily May to September, weather permitting, at the Cochrane Ranche Historic Site (Hwy 1A east of Hwy 22) and Mitford Pond Park (west end of West Rock Road off of Hwy 22).