Use \mathbf{..} instead of {\boldmath ..}. The following minimal example

\documentclass{article}
\usepackage{mathptmx}% http://ctan.org/pkg/mathptmx
\DeclareMathAlphabet{\mathbfit}{T1}{ptm}{b}{it}
\showoutput
\begin{document}
aaa\textbf{aaa}\textbf{\textit{aaa}}
$aaa \mathbf{aaa} \mathbfit{aaa}$
\end{document}
lists the output fonts as
Completed box being shipped out [1]
\vbox(633.0+0.0)x407.0
.\glue 16.0
.\vbox(617.0+0.0)x345.0, shifted 62.0
..\vbox(12.0+0.0)x345.0, glue set 12.0fil
...\glue 0.0 plus 1.0fil
...\hbox(0.0+0.0)x345.0
..\glue 25.0
..\glue(\lineskip) 0.0
..\vbox(550.0+0.0)x345.0, glue set 539.77744fil
...\write-{}
...\glue(\topskip) 5.27003
...\hbox(4.72997+0.16492)x345.0, glue set 239.18018fil
....\hbox(0.0+0.0)x15.0
....\OT1/ptm/m/n/10 a
....\OT1/ptm/m/n/10 a
....\OT1/ptm/m/n/10 a
....\kern 0.0
....\OT1/ptm/b/n/10 a
....\OT1/ptm/b/n/10 a
....\OT1/ptm/b/n/10 a
....\kern 0.0
....\OT1/ptm/b/it/10 a
....\OT1/ptm/b/it/10 a
....\OT1/ptm/b/it/10 a
....\kern 0.0
....\glue 2.5 plus 1.49998 minus 0.59998
....\mathon
....\OML/ztmcm/m/it/10 a
....\OML/ztmcm/m/it/10 a
....\OML/ztmcm/m/it/10 a
....\hbox(4.72997+0.13994)x15.0
.....\OT1/ptm/b/n/10 a
.....\OT1/ptm/b/n/10 a
.....\OT1/ptm/b/n/10 a
....\hbox(4.555+0.13495)x15.0
.....\T1/ptm/b/it/10 a
.....\T1/ptm/b/it/10 a
.....\T1/ptm/b/it/10 a
....\mathoff
....\penalty 10000
....\glue(\parfillskip) 0.0 plus 1.0fil
....\glue(\rightskip) 0.0
...\glue 0.0 plus 1.0fil
...\glue 0.0
...\glue 0.0 plus 0.0001fil
..\glue(\baselineskip) 23.18011
..\hbox(6.81989+0.0)x345.0, glue set 170.0fil
...\glue 0.0 plus 1.0fil
...\OT1/ptm/m/n/10 1
...\glue 0.0 plus 1.0fil
As a reference, see Bold italic vectors.