For most purposes, the federal criminal code applies
In Canada, the criminal code is national rather than adopted province by province, although provinces and municipalities have some authority to sanction conduct in some way or another outside the criminal code, such as the Wildlife Act and regulations under it.
Also, municipal bylaws might not address shooting a bow and arrow on its face, but might instead regulate land use in general and state that only certain activities are authorized on a particular parcel of land and those activities may not include, for example, target shooting of bows and arrows or "recreational activities".
The Reasons You Are Using The Bow and Arrow Matter
You really need to consider the purpose for which the bow is shot, because while there isn't a general prohibition, there are prohibitions applicable to most reasons for using them.
If you are dueling
If it was part of a duel, that would be a crime in Canada. R.S., c. C-34, s. 72.
If you are subject to a prohibition order
If the user is subject to a prohibition order (the U.S. equivalent term would be a protection order), a bow and arrow could be prohibited under that order. R.S., c. C-34, s. 109-111.
If you are hunting, or if you are shooting it within 200 yards of an occupied building
Even if target shooting is not regulated or prohibited in a municipality, you would ordinarily need a license to hunt anything under the applicable hunting regulations of Alberta. In particular:
Hunters must possess a valid Wildlife Certificate and the applicable
hunting licence to hunt big game or game birds.
This includes bow hunting. And, as you note, Section 52 of the Wildlife Act, which prohibits shooting within 200 yards of an occupied building (unless it's your own). Realistically, there aren't many places in an urban municipality that are not within 200 yards of an occupied building.
If your conduct endangers the public or obstructs others rights
In many circumstances, shooting arrows with a bow could constitute a common nuisance. R.S., c. C-34, s. 180.
180 (1) Every one who commits a common nuisance and thereby
(a) endangers the lives, safety or health of the public, or
(b) causes physical injury to any person,
is guilty of an indictable offence and liable to imprisonment for a
term not exceeding two years.
(2) For the purposes of this section, every one commits a common
nuisance who does an unlawful act or fails to discharge a legal duty
(a) endangers the lives, safety, health, property or comfort of the
(b) obstructs the public in the exercise or enjoyment of any right
that is common to all the subjects of Her Majesty in Canada.
If you threaten to hurt a person or animal without justification
Likewise, if you aim your bow at someone with an arrow nocked without this justification, this probably constitutes a criminal offense called "unlawful threat", R.S., c. C-34, s. 264.1, which is an unlawful threat and a crime when one:
in any manner, knowingly utters, conveys or causes any person to
receive a threat
(a) to cause death or bodily harm to any person;
(b) to burn, destroy or damage real or personal property; or
(c) to kill, poison or injure an animal or bird that is the property
of any person.
If you hit a person or animal without justification
Even if you don't intend to hit a person or animal, if you do, it would probably at least constitute the tort of negligence, and probably criminal negligence, R.S., c. C-34, s. 219-221, or assault with a weapon causing bodily harm, R.S., c. C-34, s. 267, or aggravated assault, R.S., c. C-34, s. 268, or homicide, R.S., c. C-34, s. 222 an 229, or injuring or endangering animals, R.S., c. C-34, s. 445, depending upon the circumstances. The definition of weapon in one related statute would probably apply and would cover a real (as opposed to a toy) bow and arrow, even though it is technically restricted to a particular statutory section R.S., c. C-34, s. 270.1(2).