First of all, welcome aboard.
Second, yes a ten-gallon tank is too small for most Ranids, the family which North American bullfrogs, Lithobates catesbeianus belong to. Their legs are quite powerful and they can launch them themselves quite some distance when startled or frightened. I have seen them jump off of the surface on my swimming pool and on to the deck, which is at least eight inches higher than the surface of the water. So with a small tank like a ten-gallon, a bullfrog is likely to hurt itself by crashing into the sides of the tank.
The kiddie pool is a decent idea. The problem it is how do you keep the frog in. How are your carpentry skills?
What you could do is build a box a few inches longer, wider, and taller than the pool. Line the box with a tarp to prevent the wood from rotting, place the kiddie pool in the center. Fill the areas around pool with either clean potting soil or coconut bedding. You may want to cover this substrate to prevent the previously mentioned materials from being tracked into your pool.
Next build the frame work to a screen mesh box that will fit over the top of your first box. Remember to build an access door somewhere in you mesh box. You should design mesh box to be removable for maintenance. Also, you might want to paint the wood work with a nontoxic, water proof paint before stretching the mesh over it. Same goes for the lower half of the enclosure.
Once set up you can add some plants, providing you have light over the enclosure. Water lettuce is nice floating plant for the pool, as is duckweed. Java moss is a tough hardy plant that will grow in the pool and attach itself to the pool itself. There are some nice submersible filters that would maintain the water quality of the pool. I personally use Dueto filters from Marineland, Petco carries them.
Also, if you want to add a "cool" buddy for your frog, albino bullfrogs are available. Just make sure they are very close in size and you quarantine any new frogs for 30 days before adding them to your established population.