I am ignoring the "গত রাত্রি আমি" part, as that is obvious, and tackling only the verb, which is giving you troubles.
Idiomatically speaking, the first sentence means - "I stayed in bed", or more literally "I stayed in the lying position". The second sentence means "I kept on lying down", i.e. "I carried on with the act of getting into the lying position (from, say, a sitting posture)". I believe, in Hindi "maiN leTaa rahaa" and "maiN leTtaa rahaa" express the same meanings respectively (plz. correct me if I am wrong). However, I am afraid, that the second form is not commonly used for this verb in Bengali.
Important though probably obvious note: These forms belong to the "sadhu bhasa" (সাধু ভাষা) - and that too a very literary form because of the choice of the compound verb "শয়ন করা". Corresponding literary cholito (চলিত) forms would be "শয়ন ক'রে থাকলাম" and "শয়ন ক'রতে থাকলাম", or in more "normal" language - "শুয়ে থাকলাম" (sue thaklam) and "শুতে থাকলাম" (sute thaklam)|