Maxing title on one character = trouble for others?

I have a main character on which I have the Sunspear title up to tier 9. Recently, I made a Ritualist character to farm UW with, but to my horror I noticed that I can only get Sunspear bounties on that character because my rank is too high - even when this character had only 15 Sunspear points!

So, the thing to do now is do all of my exploring in HM. But since the bounty givers already treat me as if I'm at tier 8-9, what would happen if I maxed the title on my main character? Would they stop giving bounties at all?

It's because you're ritualist's LEVEL is too high to gain SS rep points in those areas where it's denied. Your other character's SS rank has nothing to do with it.

The Sunspear title is individual for each character. What title one got won't affect the others.
But foreign characters not from Elona such as your Ritualist are already regarded high rank by the game mechanisms and can't get bounty in the starter areas. If you want to progress much more in the ranks you will have to go hardmode. A good way is to play the game until you reach Remains of Sahlajah. There you can farm sunspear and lightbringer points riding wurms quite easy even in hardmode. Use the quests A Show of Force and Requiem for a Brain (look them up on wiki) to get even more points.

As a Rit or other non-Elonian character, an easy way to gain fast sunspear points is by repeating the initial attacking waves in A Land of Heroes. Each kill gives you 4 points + a boss that givs you 50. You won't gain any points if you start this quest with 1000+ sunspear points, so the most optimal is to just restart it over and over until you have 999, then restart and complete the quest. Initial waves of attackers always give 130 points total.

Also, once you get your character to the NF mainland you will be eligible for the Sunspear bounties again in NM (to level 8 of course) or HM.

Or simply go HM outside Kamadan or Sunspear Great Hall, most mobs comes single which your spirits would utterly destroy.

You should also be able to get bounties in NM in Issnur Isles and Mehtani Keys on non-nightfall characters - I've used the Skale Hunt bounty to farm skale for Sunspear points with a non-nightfall character in the past.. so unless that has changed, it should be an option for you.