Mary P , I have spent a long time worrying about this question. Drafting replies and then deleting them lest it sound as if I am bossing you about or imposing a contrary view.
But it is not just that the horse might injure himself, he might injure you, so I will give my position.
Yes, it was I who after a whole summer of hacking suggested that when we rode the RS ponies fresh from their day of rest, it would be more rewarding to go on a long fast hack than calming them down with a slow granny ride, which had been my tactic for the previous weeks.
That was the context. My riding forward was only on a pony that is listening to me and I am confident will listen too in canter.
Your posts suggest that Bailey is dictating to you, in the saddle or on the ground. This doesn't sound good.
My summer and the change in my riding began when I watched Richard Maxwell at a clinic and adopted his routine preparation of a horse, ensuring it is safe to ride and to hack. Maxwell compares this to MOT for a car - He says that you wouldn't take a car out on the road without good brakes and steering and the same goes for a horse.
Maxwell's approach involves asking for basic turns, turning the head and quarters in both directions with decisive aids (using rein and leg on the same side), followed by backing up. It isn't pulling on both reins or using a fierce bit - but it is giving visible cues and expecting a prompt reaction from the horse. The sort of cues to which a subordinate horse would have to respond in the herd. Any insubordination or spooky inattention from my fav. mare this summer, I applied this drill. With some rigour, and it worked. It worked for me too because psychologically it put me in charge of her, and she relaxed because I had imposed my leadership.
Any horse that rushed out of the yard, regarding me as passenger - Turn, turn, back up.
If you decide Bailey isn't manageable to ride and you want to do ground work, Maxwell uses a similar routine from the ground, backing up and moving the quarters over. Bailey should respect you on the ground and not haul you along.
Maxwell uses compliance in turns and backing up, he says, because turns and backing up are not natural movements for the horse. So you are demanding compliance in the most difficult moves. It is natural for the horse to run straight and you as rider will have more difficulty stopping a horse on the straight - either out hacking or going large round the school.
So letting Bailey cue you into fast riding, with his body straight, gives HIM all the advantages.
Only after you have his compliance can you decide whether to work him fast or slow, and that surely depends not only on how he feels but on how you feel too?
On the other hand, if Bailey is over fresh because he has been cooped up all day and is being fed so much it produces too much energy - then you are facing a problem created by the owner.
And may be he isn't a safe share for you?
Maxwell's bottom line is that a horse must be safe and responsive before you entrust yourself to going fast and straight on its back.
And I have been more authoritative with the horses and much happier since I applied this tuition / test.