"It is time for bed."
Translation:Il est temps de dormir.
No. There are rules for begining a statement with "Il est" and "C'est". This case is definitely "Il est temps de dormir" and not "C'est temps.."
Its a great question. As it turns out, the answer is to do with use of the verb "temps". There's a longer complicated answer or a shorter one (i.e. mine). In French Longer explanation.
Basically, if the amount of time in question is known, or presumed to be known, we use "de". Here "time for bed" or "its bedtime" implies the time is known. If the timeperiod is unknown we can use "pour" - "This movie has how much longer to go? ... Ce film a combien de temps pour aller?"
Its to do with the impersonal expression. When "il est" is used as an impersonal expression, it does not have a subject so the construction tends to be Impersonal expression [il est] + adjective [temps] + preposition [de] + infinitive [dormir]. So "temps" here is an adjective not a noun.