Will an amaryllis bulb that has been forced bloom every year or every other year?

There are two separate situations in your questions. First, if you buy a bulb in the fall, for Xmas blooming. That bulb has been specially grown, and then forced into an early dormancy, to produce spectacular blooms. After that first home bloom, the bulb is completely depleted of energy. You will probably notice that the bulb feels soft and the diameter is much smaller. That bulb needs to replenish and rebuild before it will bloom again. It may produce only leaves for a summer or two, as the bulb plumps up again. It may even produce an offshoot before it blooms again. The second situation: You have had a bulb for a while, and are bringing it inside each fall, to force dormancy in order to have it bloom inside during the winter. As long as the bulb is growing well in the summer with adequate sun, water and fertilizer, it should bloom each year. Cultivars of the "cybister" group of Amaryllis don't always bloom every year, so that's a different story.
I get a lot of questions about non-blooming amaryllis. They seem healthy with plenty of leaves, but they don't bloom. I tell people to give them more sun. In the deep South they do very well with sun until about 2PM. In a more Northern location, they can take a bit more sun. If the leaves start to burn, that's too much sun.

we have only second types of bulbs. Wherever you buy them, they will first produce a lot of leaves, and might bloom in February-March. And locals have green leaves all year around.

I usually buy 1 to bring to bloom inside my home for Christmas or January. I then plant it outside in spring to grow on. They usually bloom in spring of the next year.

Thank you all for your responses. The bulb in question was purchased in the fall on '17, bloomed in January '18 and put outside in the spring to grow on and rejuvenate the bulb. In late September I brought it in and stored it to force dormancy for winter blooms this year. I did this with 3 bulbs (purchased at the same time) and this is the only one that did not put out a bud. It hasn't grown any leaves either. The bulb grew large over the summer and produced an offshoot so it seems to be in pretty good shape. Just no growth yet. I may be worrying too much and will see something develop later on this year.

Hello Susan, my amaryllis does that often, skips a season. Oftentimes it is one of the plants I threaten to uproot if it does not bloom and then I have to reconsider when it finally is active again. I know this bulb is in too much stress here in my garden since our conditions gets into very long dry months with very poor humidity levels.

But typically it is more towards Spring that it blooms again.

Susan, don't give up on that bulb. It may just be very slow to break dormancy. The fact that it did produce an offshoot means that it was healthy when it went into dormancy. I suggest not watering it until you see some top growth. It may bloom in late spring (its normal time if it was outside) or it may decide to skip this year.

Ditto what Barbara said. Hang in there.

All of your comments are so appreciated. It's exactly what I wanted to hear!!

I love to hear others also - I learn so much that way!

I agree with others. I once (one time!) bought a kit from a bargain box store. That bulb sat in the pot for months (I forget how many, but it was quite a while), then sent up leaves and a flower stalk, which was rather lovely. During all the time it was just patiently growing roots and getting ready.