I believe you buy it in the hotel at night like the other costumes, but it only shows up after you get the first scene where you're thinking about it. I think it was 20,000 or so. :)
Step 1: Make sure you are already dating Shiba.
Step 2: Top him in bed at least once.
Step 3: Build up your love points and keep spending time with him. You want the love gauge to be at least at around 60% (ask the fundanshi in the park).
Step 4: See both the VA school event that leads to the showering CG and the event at the agency that leads to him cleaning his room.
Step 5: See the VA school event that leads to Chiba meeting a dog. This unlocks the dog costume for purchase.
Step 6: Go to the love hotel at night (not on a date) and buy the dog costume.
Step 7: Spend time with him at the VA school and enjoy!