FYI...the registration (and collection requirements) have already been posted...but here they are straight from the BC PST legislation
http://www.bclaws.ca/civix/document/LOC/complete/statreg/-- P --/Provincial Sales Tax Act [SBC%202012]%20c.%2035/00_Act/12035_08.xml#section168
172 (1) Subject to subsection (2), a person must be registered under section 168 at the time the person causes tangible personal property to be delivered in British Columbia if the person is located in Canada but outside British Columbia
and, in the ordinary course of business, does all of the following:
(a) solicits persons in British Columbia for orders to purchase tangible personal property,
by advertising or any other means;
(b) accepts orders to purchase tangible personal property,
if the orders to purchase originate from locations in British Columbia; [ie, sales agents in BC]
(c) sells or provides tangible personal property to a person in British Columbia for use or consumption
(i) by the person,
(ii) by a third person at the expense of the person to whom the property is sold or provided,
(iii) by a principal for whom the person acts as agent, or
(iv) by a third person at the expense of the principal for whom the person to whom the property is sold or provided acts as agent;
(d) causes the tangible personal property described in paragraph (c) to be delivered in British Columbia.
(2) Subsection (1) does not apply to a person if the person sells or provides only tangible personal property that is exempt from tax imposed under this Act.
Note that ALL the requirements must be met, and they must be met in the ordinary course of business. Advertising online is not soliciting offers in BC anymore than it is soliciting offers in Australia. By the way...even if you thought you were advertising in BC, unless the orders are actually procured in BC by agents in BC, you're not required to register.
Sales taxes, and income taxes in general, require some type of physical presence within the jurisdiction before taxes apply. Unless you have a physical presence in BC, you're ok.
By the way, if you've been collecting BC PST, there is no provision within the Act to remit this to the CRA. Tax collected by unregistered vendors MUST be remitted to the BC Minister of Finance. Are you even registered with BC to collect PST? Or have you been remitting it to the CRA this whole time?