一份標書已用公司信紙,和有董事簽名,是否一定須要有公司蓋章,才算有效?

In normal case, the tender form must be signed by an authorised director together with the company's chop to confirm that he is acting on behalf of the limited company, a separate legal entity.
However, you have to check to the requirement as stated in the tender form for company's signatory. In some exceptional circumstance, the common seal of the company is required.
To conclude, check the requirement stated in the said form. Phone the party up for clarification if you are in doubt or your tender form will then be invalid.