Is flowers nectar secreation influenced by bees/pollinators?
In short, yes, it seems many flower species have mechanisms to replenish nectar after removal. For example, in Luo et al. 2014 Journal of Pollination Ecology,  9 of 11 species of plants they studied in the Colorado Rockies showed significant additional nectar production after some nectar was experimentally removed. Furthermore, the magnitude of this behavior was greater for flowers known to be heavily visited by bees:

https://www.researchgate.net/publication/268523373_Stimulation_of_flower_nectar_replenishment_by_removal_A_survey_of_eleven_animal-pollinated_plant_species