Aericsteele’s D&D 5e Questions & Support - Page 2 The Maker says...
I disagree, Malcombshaw; in my view alignments do not necessarily equal bonds. A bond is something that is important to the character; what they are willing to fight for if you will. Alignment deals more with the characters philosophy or approach. For example, whether the character believes that the ends justify the means. The Players Handbook describes alignment as something "Which broadly describes… moral and personal attitudes."
Bonds, on the other hand "Represent a character's connections to people, places, and events in the world." Two characters could have very similar bonds, but opposing alignments; or very similar alignments but conflicting bonds.
Ideals I think are more closely related to alignment than bonds are. That's not to say that bonds have no impact on alignment, but I don't think that bonds and alignments are the same thing or that one equals the other.
KNtoran, you can play without the Players Handbook but it is a bit more restricted if you do. The character generator will generate a basic character for you, but your options are very limited.