Try Jacksons Earl Grey. The bergamot is VERY subtle in this blend. It is available as loose leaf tea and as tea bags. Jacksons has become more difficult to find in recent years, at least in my neck of the woods, but you can purchase it online at
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I have purchased my tea from this website for many years. They are very efficient and reliable and I have not found any prices to beat theirs.
Jacksons claims that their Earl Grey formula is the original one, although this is disputed by Twinings.
I know what you mean about the bergamot being overpowering in many blends. It's why I won't drink any Earl Grey that isn't made by a British company. I was visiting one site the other day and they were proudly promoting that their Earl Grey was blended for American tastes. I immediately lost interest in trying it right after reading that.
Good luck.