To a Lady who having desired me to compose somthing upon the foregoing Subject ["Venus who did her Bird impart"] prevail'd with me to speak the four first lines extempore and wou'd have had me so proceeded in the rest which I sent to her at more leasure with the following verses."
Finch says that good poetry is not written on command: even Prior, whom, she says, she met on the day the poem was demanded, would not have done well. She was made uncomfortable when put on the spot. She is not a performing bear (or elephant). Her poetry is not the kind of "commerce" for ready sale in Pall-mall or the city. An interesting detail about her dress: she implies she often wore a "blue hood."
Between April and June 1715 (after Prior's return to London and before his imprisonment); McGovern dates this poem between 1706 and 1711 when Prior also visited England, but I suggest the later period after Anne Finch's publications in 1709 and 1713 when her fame had spread or after 1714 when she was frequently in London make the later period more likely.