Good quality loose leave tea is often easy to make so it both have full flavour and not a hint of bitterness. Cheap quality leaves tend to contain a lot of bitter components that easily are extracted.
So if you are prepared to experiment a little and spend a little money in order to have a good morning experience, then I suggest you find a good online tea-dealer and sample some good quality loose leave tea.
I suggest trying some in the £10-15 per hundred grams range but don't buy 100g, just buy the smallest amount possible like 20g or 50g. Try 3-4 different teas. Good quality tea can easily be had for less but in that range the tea tend to be really tasty and good examples of their type. Once you found out you really like e.g single estate Assam or Tie Guan Yin Oolong tea, it is easier to tune in on cheaper everyday versions of acceptable quality.
Green teas are meant to be drunk without milk. I like green tea but it is a much more subtle taste experience than black tea. Still, I think green teas are a good match for fasting in the morning since they can be really gentle and subtle while still refreshing (they can contain a lot of theine/caffeine).
Green teas may be a little more difficult to make since they usually require around 80C water, but they are often very economical since multiple infusions are possible. Many good green teas can infuse for a long time without producing bitterness.
If you are new to green tea try ones described as "floral/flowery" rather than "grassy/herbal" in taste at first. No particular recommendations, but Chinese green tea is probably a good starting point. Great for drinking all day long including with food.
Quality jasmine scented green teas don't contain any traces of the jasmine plant, only its scent (the Jasmine is pressed together with the tea, then removed), so no flowers. If interested, then you can't go wrong with Chinese jasmine "Dragon Pearls". Never had a hint of bitterness with any version of this tea. Goes well with lots of Asian food.
Oolongs are semi-green teas. They are usually more forgiven with temperature, and multiple infusions are possible. A step up from green teas if you want more "punch" and direct taste. Taiwanese/Formosa Oolongs are highly regarded. Personally I like Chinese "Tie Guan Yin" Oolongs from the Fujian province. It is spelled in a million different ways, but if "Iron Buddha/Goddess" or "Merciful goddess" or "Anxi" is mentioned, it is probably a "Tie Guan Yin". Don't buy it too cheap, since it comes in many grades. Goes well with food too.
Quality Darjeeling are also usually best without milk. Good Darjeeling really is exquisite but the demand for tea from this district also means that good quality Darjeeling is hard to source at low prices. (It is estimated that at least 40% of all tea in the world labelled "Darjeeling" is fake.). If interested, then a 2. flush, single estate Darjeeling in "TGFOP" leaf grade or better described as having "Muscatel" taste, is good introduction. 1. Flush are finer and more refined (as a general rule), but also more expensive.
Use a timer for Darjeeling, since many are rather strict when it comes to infusion time. Sometimes even 30 seconds can make a big difference. I have tried several Darjeelings that could be infused more than once with good results.
Assam teas have the well known rich "malty" taste, and are usually associated with drinking them with milk and or sugar. However, I have tried several Assams that are so good I prefer them without milk. Use a tea timer for Assam. There are many caveats regarding recommending tea, but a 2. flush Assam from "Mangalam" in at least "TGFOP" leaf grade or something similar is worth trying.
High leaf grades isn't the same as good tea, or tea that you may like better, and the amount of grading systems from region to region is bewildering. The point is simply to avoid leaf grades with "B" for "Broken" in them like "GFBOP". Such a "GFBOP" graded tea may be a really good tea, perhaps better than another "SFTGFOP" graded tea, but "Broken" leaves indicate a higher chance of bitterness, something you say you want to avoid.
Another problem with buying tea is that even the same tea bushes from the same field, produces different quality tea when plucked 10 days apart, with even bigger differences between every year. So good tea is less about well known tea estates or districts or tea names like "Dragonwell" or "Monkey Picked Ti Kuan Yin", than having a good tea vendor that ensures you get your "Mao Feng" tea at an acceptable price and quality every time. So choose the tea merchant before tea brand names.
If you find you like green tea/Oolongs but would like to make multiple infusions easy then this teapot is perhaps worth trying:
https://www.siam-teas.com/product/tea-maker-991/ Make one cup at the time with perhaps just 30 second steeping time ("Gongfu"style ). Despite being rather gadget like, it makes tea making easy, something I like.
I am always vary with recommendations, but I bought some teas from this vendor some years ago and found the quality good:
http://www.highteas.co.uk/This vendor is on my shortlist for my next purchases because of its good reputation and because they sell sample boxes:
https://www.siam-teas.com Sorry that this became so long. The tl/dr is; sample some high quality loose leave teas from a good vendor.