I have a similar house, and here is what worked for me (I did this when
the bathroom walls were removed for a remodeling, but I think it could
have been done with the walls in place, although you would need access
to the top of your current supply line.

Install a second line between the top of your current supply line and
plumbed to the bottom of your water heater, forming a loop. Put a check
valve in where convenient to limit water flow to one direction. Put
insulation on the original line. The loop will be filled with hot water
so you will have instant hot water in the bathroom. When idle, there
will be slow circulation of water, rising in the insulated line, and
returning, slightly cooler, in the new line.

The advantage is there are no pumps, etc, to break. The disadvantage is
possible energy loss, in that you will be creating in effect a radiator,
which will allow heat into the house (since I air condition less than
three months of the year, I don't see this as a problem; it is actually
supplemental heating in the winter. If it was a problem, I would put a
shutoff valve in the line and give up my instant hot water during the
summer months). Difficulty of installation could be a problem,
depending on your house. When I had this done, the plumber had never
heard of it and actually invited some cohorts over to see it. They even
had a wager on whether it would work. It did.

I know you can find sites on the web selling pumps that perform a
similar function, but I like to try to keep things simple and avoid
extra equipment that has a potential to break.

Aaron Fude wrote:
Hi,

I have a three story house with a water heater in the basement. I go
to the bathroom on the top floor to brush my teeth. It takes about 30
seconds or more for the water out of the faucet to become warm. Is
there a robust solution that would shorten that time to about 5
seconds?

Many thanks in advance,

Aaron Fude