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It will bloom next spring. Many perennials focus on root growth the first year; flowering requires a lot of energy which new roots just can't provide. Also, too much nitrogen fertilizer stimulates green growth which diverts energy away from flower production. If you improved the soil before planting, a top dressing of compost is adequate nutrition for bee balm.

More than likely it has too much nitrogen in the soil, or it could be that the soil is too acidic. Apply dolomitic lime to the soil, and this should take care of the issue. If it continues, then you may add a fertilizer heavy in phosphorus and potassium.

Seeds need to go through a period of cold storage to get them to germinate. Most seed companies do this for you. If seed was collected this fall, separate the seeds from the chaff and let them air dry for a few days. If you are sowing indoors, store the seed in a glass jar in the refrig for 2+ months. Some sites advocate "moist stratification"; there is disagreement on this point. It takes 2-3 weeks for seed to germinate and then 2 months to reach planting size. 95% of seeds germinate. Here is a resource: https://npn.rngr.net/renderNPNProtocolDetails?selectedProtocolIds=lamiaceae-monarda-95&referer=wildflower

First year perennial plants often don't bloom as they are focusing on root establishment but I'm a bit surprised that your bee balm didn't show a flower. Is it in full sun and moist soil? Apply compost to the surface yearly; this is the only fertilization bee balm should receive. Too much nitrogen yields lots of green growth and few flowers.

It can in the right area. What climate zone are you in? This will help me to recommend plants that are suitable for your area.

I'm not a fan of this approach but you can give it a try and see how the plants respond. It will tell you if it isn't happy by under-performing. Bee balm likes moist soil and spreads slowly via above-ground stolons. The fabric will be an impediment to spreading out so it is likely to get very crowded. This makes it prone to powdery mildew. Landscape fabric has other problems. It doesn't stop weeds; it just makes it much harder to pull them. It reduces the amount of water and air that reach the roots. The rocks heat up under the sun and increase soil temperature. This isn't good for soil moisture (warmer soil evaporates faster) and it isn't good for plant roots. You can tell I'm a fan of starting with a clean planting bed and using mulch. 3 inches of compost or wood chips - or any other plant-based material - will suppress weeds, help retain moisture and slowly improve your soil as it breaks down. Enjoy your bee balm.