Thanks for your question.
Theft is the dishonest appropriation of another's property with an intention to permanently deprive the owner of his property.
The elements of this offence need to be proved beyond all reasonable doubt. The burden of proof is very high. It is the owner of the bike who must prove this.
I think your offer to pay back the value of the bike is reasonable. If the owner does report this you can explain the circumstances as to how you lost the bike and have offered to compensate for the owner's loss.
It is a civil matter until the owner decides to report to the police.
To add, the police will only pursue the matter if they can establish there is theft and sufficient evidence to satisfy the high burden of proof required.