Sorry Fountainhall: The 'the deep-rooted, age-old respect for elders' does not extend to anyone giving up their seat on a bus or train for them, unlike in The UK. So it's a meaningless respect as it exists in words only. And perhaps your bowing was most correct or perhaps it wasn't. The Japanese would be very unlikely to tell you if it was the latter for the very reasons we've been discussing. Fitting in does not and has never meant aping, It means both sides accepting the others foibles.

Are you seriously saying you mastered this? Because I find that hard to believe.
From Wikipedia on Japanese etiquette.

Bowing
Main article: Bowing

Bowing (お辞儀 o-jigi?), is probably the feature of Japanese etiquette that is best known outside Japan (the o お is honorific but cannot be omitted for this word). Bowing is considered extremely important in Japan, so much so that, although children normally begin learning how to bow from a very young age, companies commonly provide training to their employees in how to execute bows correctly.

Basic bows are performed with the back straight and the hands at the sides (boys and men) or clasped in the lap (girls and women), and with the eyes down. Bows originate at the waist. Generally, the longer and deeper the bow, the stronger the emotion and the respect expressed.

Bows can be generally divided into three main types: informal, formal, and very formal. Informal bows are made at about a fifteen degree angle or just tilt over one's head to the front, and more formal bows at about thirty degrees. Very formal bows are deeper.

The etiquette surrounding bowing, including the length and depth of bow, and the appropriate response, is exceedingly complex. For example, if the other person maintains his or her bow for longer than expected (generally about two or three seconds), it is polite to bow again, upon which one may receive another bow in return. This often leads to a long exchange of progressively lighter bows.

Generally speaking, an inferior bows longer, more deeply and more frequently than a superior. A superior addressing an inferior will generally only nod the head slightly, while some superiors may not bow at all and an inferior will bend forward slightly from the waist.

Bows of apology tend to be deeper and last longer than other types of bow. They tend to occur with frequency during the apology, generally at about 45 degrees with the head lowered and lasting for at least the count of three, sometimes longer. The depth, frequency and duration of the bow increases with the sincerity of the apology and the severity of the offense. Occasionally, in the case of apology and begging, people crouch down like Sujud to show one's absolute submission or extreme regret. This is called Dogeza. Even though Dogeza was previously considered very formal, it is mostly regarded as a contempt for oneself today, so it is not used in an everyday setting. Bows of thanks follow the same pattern. In extreme cases a kneeling bow is performed; this bow is sometimes so deep that the forehead touches the floor. This is called saikeirei (最敬礼), literally "most respectful bow."

When dealing with non-Japanese people, many Japanese will shake hands. Since many non-Japanese are familiar with the custom of bowing, this often leads to a combined bow and handshake which can be quite complicated to execute. Bows may be combined with handshakes or performed before or after shaking hands. Generally when bowing in close proximity, as necessitated when combining bowing and shaking hands, people turn slightly to one side (usually the left) to avoid bumping heads.