We strap ours to our swim platform as well underway. Then let it float tied to the boat when we're sitting in a cove or just lounging. We have a battery powered air mattress pump we used one outing to inflate our towable once we had gotten out on the lake. That worked okay, but if I we're gonna deflate to travel and inflate at the next spot I would recommend a plug in style air pump. There is room under our sun pad for ours when we're finished for the day.
By the way the boat in my sig pic is not the one we use for towables. The Stratos inboard outboard is the one we ski with.