Blackboard bold characters

This doesn't exactly answer your question (how to use bbold with AMS's black board bold characters). I believe that would require some TeX incantations.

A cheaper work around is to use either the package bbm or the package doublestroke. The former defines the \mathbbm command and the latter uses the \mathds command, so they don't conflict with the AMS \mathbb. Also asthetically I prefer the bbm fonts over bbold since the latter is sans serif, which doesn't quite fit in right against the AMS serifed fonts.

I had the same question about a year ago. I came up with the following solution, which seems a bit cleaner that Juan's "hack":

\DeclareSymbolFont{bbold}{U}{bbold}{m}{n}
\DeclareSymbolFontAlphabet{\mathbbold}{bbold}

Then one can use $\mathbbold{1}$ (and I store this, without the dollar signs, in the macro \ind since I use it as an indicator function).

You've already got a pretty good answer. Just in case you really wanted to use amsmath and bbold, the following TeX-hack seems to do the trick.

\usepackage{amsmath}
\usepackage{amsfonts}
\makeatletter
\def\amsbb{\use@mathgroup \M@U \symAMSb}
\makeatother

\usepackage{bbold}

\begin{document}
$\mathbb{1}, \amsbb{X}$
\end{document}