This XAML will work fine, but its limiting (it won't allow you to set the color of the text displayed, as requested):
<dxb:BarStaticItem
Content="{Binding MyStatusBarText}">
</dxb:BarStaticItem>
This particular control does allow us to set the ContentTemplate. We can use this to style the content:
<dxb:BarStaticItem
ContentTemplate="????">
</dxb:BarStaticItem>
First, we define a DataTemplate in Window.Resources. This is what our ContentTemplate will point at:
<Window.Resources>
<DataTemplate x:Key="MyStatusBarContentTemplate">
<!-- As the DataContext of a resource does not default to the window, we have to use RelativeSource to find the window. -->
<TextBlock Name="MyText"
Text="{Binding Path=MyStatusBarText,
RelativeSource={RelativeSource Mode=FindAncestor,
AncestorType=Window}}">
</TextBlock>
</DataTemplate>
</Window.Resources>
As the DataContext of a DataTemplate is different to the rest of the XAML, if we omit the XAML RelativeSource={RelativeSource Mode=FindAncestor, AncestorType=Window} then the binding will not work properly. Other than that, all we are doing is defining a template which can be used to render the contents of the control.
Then, we point our control at this DataTemplate:
<dxb:BarStaticItem
ContentTemplate="{DynamicResource MyStatusBarContentTemplate}">
</dxb:BarStaticItem>
Now that we have defined a custom data template, we can do anything we want. For example, we could add a Converter which colored the text red if the status bar contained the text Error (something that was impossible, otherwise).
This answer also illustrates how it is possible to use a DataTemplate to display custom content for most controls.
Update
Rather than defining the DataTemplate in the resources for the Window, defined it as a resource for BarStaticItem. This keeps related items together in the XAML.
This particular XAML means that the status bar text automatically goes red if the text contains the string Error, and the status bar text is automatically prefixed with the time. Let me know if you want me to post the C# code for the converters.
<dxb:BarStaticItem
ContentTemplate="{DynamicResource MyStatusBarContentTemplate}">
<dxb:BarStaticItem.Resources>
<DataTemplate x:Key="MyStatusBarContentTemplate">
<!-- As the DataContext of a resource does not default to the window, we have to use RelativeSource to find the window. -->
<TextBlock Name="MyText"
Foreground="{Binding ElementName=MyText, Path=Text, Converter={StaticResource ColorRedIfTextContainsError}}"
Text="{Binding Path=SettingsGlobalViewModel.StatusBarText,
RelativeSource={RelativeSource Mode=FindAncestor,
AncestorType=Window},
Converter={StaticResource PrefixStringWithTime}}">
</TextBlock>
</DataTemplate>
</dxb:BarStaticItem.Resources>
</dxb:BarStaticItem>