Mealy bugs are are soft-bodied insects with white waxy filaments protruding from the tail end. They sometimes look like they are covered with cotton, which actually are hydrophobic sappy secretions. They are one of the worst pests for bulbs. They pierce the tissue and suck the sap and carry diseases. They are especially fond of many bulbs in the Amaryllidaceae family and can crawl down in the crevices of the bulb where they are difficult to get at. Bugs are of the genera Pseudococcus, Planococcus and Phenacoccus.
There are two kinds of mealy bugs. The soil mealy bugs are especially difficult to eradicate without resorting to expensive chemicals. The Arisaema pictured in the image was struggling and yellowed very early in the season. Upon digging it the culprit was discovered. Photo 1 was taken by Arnold Trachtenberg. Photos 2-3 were taken by Nhu Nguyen showing the above ground mealybugs on Sprekelia formosissima leaf crevice.
Some people just recommend tossing the plant and the soil as well if you have root mealies. Various treatments have been tried with only short-term help but imidacloprid, a treatment that many people recommend for sucking and crawling insects, has been used very successfully. It works as a contact and a systemic and lasts from 6 to 9 months. It is sold under the name Marathon in the United States and Provado in the U.K. For over the counter this is the active ingredient in Bayer's Tree & Shrub Insect Control. The recommended rate is 2 to 3 oz. to a gal. of water dilution for that product. This product can be used for mealy bugs found in the leaves or neck of the bulbs too. (See next paragraph.) But it is recommended that it be alternated with other products so that mealy bugs will not become resistant with repeated us.
Mealy bugs that are found usually in the crevice of the leaves or the neck of the bulbs respond to less drastic measures. For those, people recommend lightweight summer oils, diluted Murphey's oil soap, straight alcohol, and a solution of 1/3rd each of water, metho (alcohol) & milk with milk as a wetting agent, or half water and alcohol. Spray or apply with a cue-tip. More than one treatment may be necessary. Vigilance is important to eliminate them before there is a major outbreak and damage to your bulbs.
Leo Martin has this suggestion: "Plants grown in containers may be completely submerged for 3-24 hours in water with very slight amounts of detergent added, just enough to create a very small amount of bubbles when agitated. This drowns mealybugs, scale and their eggs. It needs to be done at an appropriate time of the year for the plant, and the duration must be chosen carefully. It is more effective if, part-way through the dunk, you physically remove as many insects as you can with a cloth or brush. Immerse the whole plant in the pot; this also kills insects on the roots.
Plants with high levels of infestation will have many small insect piercings though which detergent may enter and cause tissue necrosis. A heavily infested plant would be better treated with several 1-hour dips at weekly intervals than one long dip. Leafy plants tolerate less submersion than non-leafy plants, and multiple shorter immersions are probably better for them than one long stretch."
Click here to see PBS list postings about mealy bugs. Here is a more recent post that includes several comments.