You can use the undocumented Bar
property of the ErrorBar
object to set the line style:
d = errorbar(1:3, 1:3, 1:3, 'LineStyle', ':');
% Make the vertical bars dotted as well
d.Bar.LineStyle = 'dotted';
% Valid values include: 'solid' | 'dashed' | 'dotted' | 'dashdot' | 'none'

Or if you just want it to be the same as the LineStyle
you specified you could also use the undocumented Line
property:
d.Bar.LineStyle = d.Line.LineStyle
For future reference, you can get a list of all properties and methods for a graphics object (undocumented or not) by obtaining the meta.class
for the object:
cls = meta.class.fromName(class(d));
% List of all properties
cls.PropertyList
% List of all methods
cls.MethodList
You can often find and modify the various pieces of a complex plot object using undocumented properties found in this way.