Yes, just buy another 2nd class Half-Fare ticket for your dog or bike.
Depending on the route, it may be cheaper to buy a day ticket.
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Note for customers without Half-Fare Card
If you do not have a Half-Fare travelcard, you must register as another person with a Half-Fare travelcard (see the section on tickets for fellow passengers) so that they can buy the ticket at half price.