a bit about spellbooks in Basic/Expert D&D. One of the rules he mentions in that post is the limit on the number of spells that a magic-user or elf can have in their spell book from page X11 of the Expert Rulebook:
"Magic-users and elves are limited to the number of spells they may know, and their books will contain spells equal to the number and level of spells the caster can use in a single day (thus, the books of a 4th level elf will contain two first and two second level spells)."
This means that magic-users and elves are pretty limited in the spells they have available to choose from everyday. If you look at the experience chart for magic-users on X6, you see that at 14th level the most spells a magic-user would have available to them is 22 spells - four each of first through fourth level spells and three each of fifth and sixth level.
Compared to every other edition of D&D this is a severe limitation on the spells available. In every other edition, the number of spells a magic-user can learn and scribe into a spell book is based on their Intelligence score. Basically, the higher your character's Intelligence, the more spells they can learn of each level. And there is no restriction on how many of those they can write into their books at a time. In AD&D, a first-level magic-user with an 18 Intelligence and access to a lot of scrolls or other spellbooks could potentially write 18 first level spells into their book. Obviously that's quite a difference from the single spell that a similar B/X magic-user has!
The only reasons I can imagine for this limitation in B/X are to limit the power of a magic-user and to keep things simple. If you have to choose your one additional spell to add to your book each level, you really need to think about what you want your magic-user to be able to do. In a sense, every magic-user in B/X is a specialist with a very limited repertoire of magic they can use. You need to consider your character's role, the spells that can help them best fulfill that role, and choose accordingly each level. Forget adding new spells from scrolls. Scrolls are just temporary things that you use, not something you keep to copy from.
There are a couple problems I see with this, though. First, this rule does not take into account the differences in characters' Intelligence. A magic-user with a low Intelligence can memorize the same number of spells as one with an exceptional Intelligence. Second, if you choose a spell for your book that the character never uses, you further limit the choices available to the character. Here's how I would address both of these issues.
To account for differences in Intelligence, let a magic-user learn additional spells per level equal to the number of additional languages they can learn. A magic-user with an Intelligence under 13 could only learn the number of spells they can cast. A magic-user with an Intelligence of 13-15 could learn an additional spell of each level, and so on. For example, a third level magic-user can cast 2 first level and 1 second level spell. If the magic-user has an Intelligence of 9, they have three spells in their book, exactly the same number and level they can cast. If their Intelligence is 17, they can learn up to 4 first level spells and 3 second level spells.
If you use the rule that characters only learn new spells when they advance in level and return to their mentor, they could gain the additional spells at that time. I would suggest rationing them out, so that the character never receives more than two new spells at a time. For instance, if your magic-user has an 18 Intelligence, they could learn three bonus spells. I would have the first bonus spell available when the character is created, essentially when they gain their first spell. I would make the second bonus first level spell available at second level when they gain another spell. So at first level the character would have two first level spells available in their book. At second level, they would have four first level spells in their book. They wouldn't gain any more first level spells (including their other bonus first level spell) until the character reaches seventh level. At that point they can cast three first level spells per day, so they would gain their third core first level spell and their third bonus first level spell, bringing their total to six.
To accommodate for a poor choice of spells as a character develops and gains experience, I would allow a character to do research to rewrite a spell in their book. To replace a spell that the character has learned, have them spend the time (two weeks per spell level) and money (1000 gp per spell level) required to research a new spell. At the end of the requisite time they can replace one spell in their book with a spell of similar level. The old spell is removed from their list. I would limit a magic-user to replacing one spell each time they gain a level, but you could allow more if they're willing to spend the time and money.
Glenn is right that B/X really doesn't need any rules changes to be a complete and very playable rule set, but I can't resist tweaking things like this a bit to give players some more options.