You have 1-2 more options you may not have considered.
First, you could turn up your main tank temp but install a thermostatic mixing valve. This lets you set your tank to, say, 120 but keeps the final output temp at a safe level. These are really easy to DIY if you're handy, or cheap to have a plumber do, and can make a tank feel 20-30% larger for <$200 (not counting labor). This is such a popular option that there is literally a product
called "Tank Booster Pro" that's not much more than a mixer and some installation goodies:
These things can make an existing 50-gal "feel like" a 60-70-gal and IMO they actually increase safety for a water heater because if there's any malfunction at all (user programming error, failed thermostat, etc) you've covered that angle as well.
You can also add a "point of use" water heater at/near the tub itself. These are kind of crappy if they're the only water heater on the line - folks building tiny homes and cabins often try to use them because they're so cheap, and are disappointed because raising a cold supply from, say, 50F to 100F still takes a LOT more energy than those folks realize (the water is flowing, so you don't have the luxury of slowly heating it in-place).
However, if your only goal is to raise 100-105F hot-supply water to say 115-120F (scalding, but hear me out), that takes a lot less energy, low enough that if you have so much as a 20A circuit somewhere to tap you may not need much for the install. Now here's the thing - you install a thermostatic mixing valve here as well. That eliminates the scald risk and drops the output to your tub-temp goal, but once again needs only 75% (depends on your settings) as much hot water input. With both tricks together you might even be able to fill that tub with somebody else enjoying a hot shower or doing dishes.
These tricks do have downsides - they take some space to install, you can still run out of hot water if you push it hard, and if you started out too cold (a guest took a really long shower before you used the tub) you still have recovery time to deal with. But one final benefit is the cost - in addition to being simple, you also aren't keeping another 40+ gallons of water hot all the time. Over the lifetime of the units that'll pay off on your energy bill, too.
One final trick if you want to go "ham" on this - some luxury homes will have very small water heaters at/near a tub like this, just to serve the tub. They're very small - 15 gallons is common - and do take some space. But they will give you that same boost as a POU unit, while taking less energy to achieve the same output, so you're still getting that 25% or so "capacity boost." Since they're so small, if you have a closet near the tub they're easy to stuff into that kind of area without losing much actual closet space, and very cheap. Vevor has one (no idea on its quality) listed at $170 and 110V/1600W so you just need a 20A circuit, which is a lot easier to have-already/retrofit in many cases than a 240V feed for something bigger...
