Change the reservoir with fresh solution at least once a week if at all possible. Just recycle the old solution by dumping on some plants outside. Drain the solution carefully so you don’t damage your plant growing in the bucket (you may want to consider adding a spigot or drainage hole to the bottom of the bucket for ease).
Roots of a cucumber plant just 20 days after transplanting.
If you maintain your system in a very sterile and controlled environment, you may be able to just add plant food and water as it gets depleted in the bucket, without ever changing the reservoir. But always maintain a pH around 6.0 and adjust your EC depending on the maturity of the plant. If you are growing a flowering plant, you will need to switch to a Bloom plant food at flowering. (since it contains more phosphorous and less nitrogen)
Overall keep an eye on your plant for insects and diseases. Always remove dying leaves and discard. With these type of passive systems it is VERY important to keep the growing area clean and disease free. With a little work, you will soon have beautiful plants growing in your home-made bubbler system!