I was able to scrounge up another plastic stage box with a snap on lid and I put that in the bathroom along with an ice cream pail. As the drain stop on the tub hasn't worked since I bought this place, I then went down to the local store and bought a tub stop for a little over $2. After doing yard work earlier today, I was done and went to take a shower but put the drain plug in place first. After the shower, I dried off and scooped out the water in the tub into the storage container. I didn't spill a drop and it took me just a few minutes to get all the water I could out of the tub.
There's enough water in the container for 3 flushes of the toilet and that's how many times I've been flushing it since I've started keeping track. Doing what you suggested with the rinse water from the washing machine and doing what I did with the shower water, I could save about 500 gallons a month. A savings of $8 a month money wise but everything I do adds up.
Next spring, it'd be rather easy for me to route the drain from the bathtub and bathroom sink into a barrel down in the basement and then by using a sump pump and hose I already have, I could pump the bathroom sink water, clothes washer wash water, and excess shower water not needed for the toilet into a another barrel outside for use in the garden. And I could do this without lugging buckets of water up stairs.