To go to Johor Bahru from Singapore, take the MRT to Kranji station. Head to the bus stop outside the station exit and board SBS Bus 170 (blue plate) to Kotaraya bus terminal, Johor Bahru. The fare is S$1.80. Keep your ticket. If you have the MRT card, tap it on the card reader upon boarding and again when alighting. The bus will not wait for you at the immigration. After immigration, follow the signs to the bus platform to board the same bus number. At Kotaraya bus terminal, walk to Jalan Trus (next to terminal) and hail a taxi to Tebrau City. The metered fare is about RM15 (red taxi). However, the same taxi will charge a fix fare to return to the bus terminal from Tebrau City, at RM25. The blue executive taxi, although charges metered fare, will cost more, up to RM37. The ride in the executive taxi is more comfortable. The fare from Kotaraya bus terminal back to Kranji MRT station, Singapore is RM1.80. Pay the driver the amount and keep the ticket until you have reached Singapore. If you have any query, the helpful bus driver can assist. Also, you can board SBS Bus 160 to go to the same destination and back.
Tebrau City is the largest shopping complex in Johor Bahru with Jusco department store and supermarket being the anchor tenant and many shopping and food outlets like Toys 'R' Us, Kenny Rogers Roasters, etc. You can shop for your groceries at Tesco which is just across the road from Tebrau City. I was informed by the blue executive taxi driver that you can get even cheaper items at Pandan City which is about two third of the distance from Kotaraya bus terminal to Tebrau City. You will pass by it on your way to the latter.