On the point of bushido and its application to Japanese warfare - there wasn't any. Bushido, as any kind of formalised concept of 'honour', was not really a thing in any sense until the late 19th century, well after the advent of gunpowder. Its conceptualisation was essentially a way to group various ideals, ethics, and so on from before - e.g. passion, integrity, etc. That being said, these were, to quote Captain Barbossa, "more what you call guidelines, than actual rules." Samurai, lords, and the like were not one homogeneous mass of honour-bound warriors pledged to serve whoever was higher than them on the food chain. Some were, some weren't, and we have well documented cases of both happening throughout the history of Japan. I'm just going to go ahead and link this thread and /u/ParallelPain because while I swear I've written a lot on this I can't find it anywhere, but that answer is great as well.

This idea of there not existing any formal code of bushido better explains a lot of pre and post gunpowder warfare in Japan. Even through the early developments of the samurai as a 'class' alongside the shogun role, and throughout the various periods of war culminating in the sengoku era, we do not see any evidence which supports the idea that bushido significantly shaped their actions. Thus, the tactics employed in warfare (wrt specifically to this question, siege warfare) were perfectly fine and justified, all things being considered.

Medieval knights saw no contrast. "Chivalry" was more of a culture than a strictly defined code one adhered to, and there was nothing in the contemporary understanding of chivalry that limited military tactics. Bribing defenders in a garrison, sneaky maneuvers, ambushes, night raids, cutting the enemy off from supplies, and other such tactics were all known, accepted, and utilized in the period. So to begin with, a siege was not considered in any way a contrast to the medieval conception of martial glory. But that aside, a siege was not purely static. Even assuming that the attackers were not making any kind of direct assault (tunneling under the walls or whatever), a besieging force would have to be ready for a possible sally by the defenders, which could result in skirmishes. The army would also have to maintain patrols and outriders, both to forage for supplies and to ensure that they would not be caught unawares by an army coming to relieve the defenders. Small unit actions like these raids and scouting patrols were extremely common in medieval warfare. It was much more likely for a soldier to have fought in a number of these kinds of actions than to have engaged in a major field battle. Even if a soldier did not have the opportunity to participate in direct combat during the siege itself, these raids, patrols, and skirmishes would provide opportunities to test one's mettle against the enemy in the field and gain combat experience.