The auditory brainstem response (ABR) is a valuable clinical tool for objective hearing assessment, which is conventionally detected by averaging neural responses to thousands of short stimuli. Progressing beyond these unnatural stimuli, brainstem responses to continuous speech presented via earphones have been recently detected using linear temporal response functions (TRFs). Here, we extend earlier studies by measuring subcortical responses to continuous speech presented in the sound-field, and assess the amount of data needed to estimate brainstem TRFs. Electroencephalography (EEG) was recorded from 24 normal hearing participants while they listened to clicks and stories presented via earphones and loudspeakers. Subcortical TRFs were computed after accounting for non-linear processing in the auditory periphery by either stimulus rectification or an auditory nerve model. Our results demonstrated that subcortical responses to continuous speech could be reliably measured in the sound-field. TRFs estimated using auditory nerve models outperformed simple rectification, and 16 minutes of data was sufficient for the TRFs of all participants to show clear wave V peaks for both earphones and sound-field stimuli. Subcortical TRFs to continuous speech were highly consistent in both earphone and sound-field conditions, and with click ABRs. However, sound-field TRFs required slightly more data (16 minutes) to achieve clear wave V peaks compared to earphone TRFs (12 minutes), possibly due to effects of room acoustics. By investigating subcortical responses to sound-field speech stimuli, this study lays the groundwork for bringing objective hearing assessment closer to real-life conditions, which may lead to improved hearing evaluations and smart hearing technologies.