Can we use FedBizOpps (fbo.gov) to request quotes "Bid Schedules" to determine competition and award for the BPA or are we expected to contact vendors who provide these services directly?
The competition requirements of FAR Part 13 apply to individual orders under a BPA, so you are correct in recognizing the need to obtain competition. Many organizations have multiple BPAs with different companies offering the same supply or service, and compete each order among the BPA holders to provide for the required competition.
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It appears from your question that you have a BPA with only one company. In order to obtain quotes from at least two other companies in accordance with the preference for at least three sources at 13.104(b), the guidance at FAR 13.303-5(d) refers to the synopsis and posting requirements at FAR 13.105. You can post in FedBizOpps, though you're not required to, as the call will be for $25K or less.
However, it's important to obtain at least two other quotes to demonstrate adequate competition. You can do this by contacting vendors directly or by posting the requirement on FedBizOpps. For future purchases you may want to set up additional BPAs, in accordance with FAR 13.303-5(d).