The following response is based solely on the question and background information provided. As we do not have all the facts particular to your contract, program, and situation, we highly recommend, as applicable, you consult your leadership, contracting officer and/or Legal Office for guidance.
Your question is centered on your use of the term "solicitation." For purposes of responding to your question, I'll use the definition assigned to the term at FAR 2.101 stating that "solicitation" means any request to submit offers or quotations to the Government. ... Solicitations under simplified acquisition procedures may require submission of either a quotation or an offer." FAR 13.303-2(d) focuses attention on the agreement instrument and alludes to that fact that certain information must be attained before establishing the agreement such as "securing maximum discounts," "documenting the transactions", etc. FAR 13.303-3 in covering the preparation of BPAs states specifically to prepare BPAs on the forms specified in 13.307. FAR 13.307(a) identifies SF 1449s as appropriate for soliciting for commercial items; however, it is nonmandatory (see FAR 12.204) when soliciting for commercial acquisitions less than the simplified acquisition threshold.
More generically but relevant to your question, it is important to keep in mind the following from FAR 1.102-4(e) which states "If a policy or procedure, or a particular strategy or practice, is in the best interest of the Government and is not specifically addressed in the FAR, nor prohibited by law (statute or case law), Executive order or other regulation, Government members of the Team should not assume it is prohibited." While the situation you described is addressed in the FAR, it appears latitude is provided to use the instrument of choice (i.e., letter). Such a letter, however, must include all appropriate BPA terms and conditions associated for the supply or service you are soliciting.
As an aside, I noted you stated "all of our BPA holders are local and FBO was not used." I have to assume that your BPA-related requirements fall within the exceptions to synopsizing (see FAR 5.202) through the Governmentwide point of entry (aka FedBizopps).