Mr WordyI would not use it in formal writing though
Sorry, I wasn't thinking very carefully when I wrote this. Having just mentioned a "plural case" I had in mind that we were talking about plural nouns, which is a little different from your example. Let me try again.
If "there is/are" refers to a plural noun then "is" is informal/conversational. For example, "There's four rooms downstairs" is informal, while in formal usage it should always be "There are four rooms downstairs".
If "there is/are" is followed by a list of different nouns, the first of which is singular, as in your example, then "there is" is acceptable and natural to me in all types of usage. For example, I would write "There is a bathroom, a dining room and two bedrooms". (Perhaps some people who are very strict about these things might insist on "are", but I wouldn't.)
If "there is/are" is followed by a list of different nouns, the first of which is plural, then we're back to the original case. "There's two bedrooms, a dining room and a bathroom" is informal/conversational, and formally it should be "There are two bedrooms, a dining room and a bathroom".