Firstly, blender tends to use the term remove instead of delete. Secondly, the armature doesn't directly store the bones, they are stored in a collection called edit_bones (at least, they are when you are in Edit Mode, which is what you script does. bones is for Pose Mode/Object Mode, but bones can't be deleted from there).
So, you firstly need to loop over the edit_bones instead of bones and then use remove instead of delete.
for bone in armature.edit_bones:
if fnmatch.fnmatchcase(bone.name, "something"):
armature.edit_bones.remove(bone)
You can easily explore the properties available on the armature using blender's Python Console, typing in your code there and pressing Ctrl+Space to autocomplete:
>>> bpy.data.objects['Armature'].data.
animation_data
animation_data_clear(
animation_data_create(
as_pointer(
bl_rna
bones
copy(
deform_method
draw_type
driver_add(
driver_remove(
edit_bones
get(
ghost_frame_end
ghost_frame_start
ghost_size
ghost_step
ghost_type
id_data
is_editmode
is_library_indirect
is_property_hidden(
is_property_readonly(
is_property_set(
is_updated
is_updated_data
items(
keyframe_delete(
keyframe_insert(
keys(
etc....
etc...
etc..
etc.
Using this, you would be able to see there is no delete method.