드셔보세요 is a two word phrase. 드셔 보세요 = 드시(다) + 아/어 + 보시다 = please try (some food). Both have the honorific affix 시 in it. Their normal forms are 들다(eat, drink) and 보다 (do something for a trial). 들다 is a highbrow version of 먹다 (to eat). You use 먹다 for yourself, your friends, children, and animals, and 들다 for people senior to you and in social settings. 시 (honorific suffix) is often added, to make it 드시다 (ㄹ drops because of irregular conjugation). Given 먹다/들다/드시다 and 보다/보시다 (and also presence or absence of 요 at the end), there are several ways to say the phrase with varying politeness: 먹어 봐(very familiar), 먹어 봐요, 들어 봐(요), 드셔 봐요, 드셔 보세요, of which 드셔 보세요 is the most polite version.