I am assuming this is to heat enough water to fill the tub as your existing tank is not large enough to handle the tub being filled? I put in a small 5 gallon hot water tank in the crawl space under my kitchen near the dishwasher and clothes washer to help with the long run my pipes are to get hot water to that end of the house and it works great. My bathrooms are at one end and my kitchen/washer are at the other end of a ranch that is over 60 ft long. I get instant hot water at the far end of the house. A simple and cheap add on for under $300. You can also consider an air tub instead of a jetted tub. Make sure your tub is well insulated to help with heat loss.

My last home had an acrylic drop in bathtub. When my plumber installed it into the deck, he wrapped the tub in insulation to help keep the water warm for a longer time.

Circulating water in a whirlpool tub just makes the hot water cool faster.

There are lots of articles about insulating tubs on the internet.

Why would you think the jets help keep the water warm , they do exactly the opposite . I have an acrylic soaker tub I have hot bath every night and while I soak I add hot water if it cools and yes we aslo insulated when we installed . No tub holds hot water forever . If you think of going tankless make sure there is as short a distance from the heater to the tub . That is why in Euprope you see the heater often in the bathroom not in the basement travelling long distance to where you want it.

My main bath has a tub on an outside wall, so I get exactly what you are talking about. When we remodeled that bath we insulated all the way around the tub, and underneath as well since we're on a slab. What a difference that made! I can actually enjoy a nice long relaxing bath now.