Out of 11 traveling companions(counting current XY cast) i have to say closest bond was definitely presented with Brock and Misty imo.
One of reasons for this belief comes from fact how Ash only cried when Brock and well more so Misty had to depart saying alot about close relationship and strong attachment they built as friends between themselves. He was visibly shaken breaking down as character revealing how much all support, laugh, enjoyment, arguings and both good and bad moments they spent together meant to him becoming like true family.
Interestingly enough out of all girls Ash traveled with, it was only Misty who started to sob being on edge of crying when brother trio teased her over that clearly not wanting to leave her friends. So theres that too.
That said if i had to choose between those two while Brock may seem like logical choice in being labeled as someone with who Ash shared strongest friendship. Due to traveling for so long together, being person to who Ash could talk to without any refrain confiding himself. Having brother type of relationship working as synchronized team together with Brock helpling Ash great deal on his journeys through advices, moral support and wise comments.
I still got feeling how with Misty there existed certain dimension, variety of emotions and level of understanding between her and Ash which with time solidified their bond and relationship to very, very meaningful level.
Because of that and reasons ill list below Misty and Ash had in my opinion most organic, endearing and filled with lot of care, tension, comedy and affluent characterization dynamic adding to realism.
From personality standpoint both Ash and Misty could/can be stubborn, sometime impulsive and hotheaded not wanting to back down to challenge or admit when they are wrong. There was always present certain competitive fire and friendly rivalry going between them encompassed through witty quips, sarcastic remarks and moments of arguing assessing each other knowledge, resourcefulness and even skills in battling taking competiton between them usually very seriously(like battle for badhe, Togepi, Totodile, Alto Mare race, Whirl Cup etc).
But they tend to be also very different from each other. Ash is clueless, naive and usually rash in decisions. Misty is more of a raconalist being blunt and straightfoward when something wont work, known to be big dreamer and romantic soul liking love and tenderness as contrast to her tomboyishness. And tend to be overly defiant, curious liking to solve riddles and be pat of action showing intelligence and quick thinking in coming up with plans how to escape of danger. Being planner, while Ash takes things as they are taking action before carefully preparing strategy leaving Misty several times astonished because of that overconfidence. But also admiring him a lot because of that being one of things she liked about him, despite not directly admitting it.
All of this created heavily emotion packed, full of energy and swaying chemistry going between Ash and Misty. With their similarities and differences making organic and spontaneous atmosphere having everything neeeded to make for ineresting relationship. Relationship wehich you could in end view as natural and unforced.
With there existing certain disagreements, getting on each other nerves or trying to outsmart themselves(which is normal for any friendship in real life with people having to learn how to live with each other flaws and find compromise). While their interactions also being pervated with lot of care, personal understanding and motivation .
With Misty raising up his spirit whenever he was depressed, or let down having many moments of laugh, talk about their desires or fun teaching Ash how to be more humble, better planner and trainer.
On other hand Ash influence on Misty stem from managing to cause conflict inside her charactere awakening that caring and tender traits putting lot of dedication and effort in helping people she cares about, spuring her brash, stubborn nature and competitive spark when getting on her nerves with his stupidity and audacious behavior .
Growing to respect, tolerate and care for each olther accepting both their flaws and qualities culminating in strong friendship. And to this day what appeared to be imo arguably closest bond so far.