Doing similar in September when the Singapore GP is on due to the exhorbitant hotel rates during this period. Staying at The Puteri Pacific Hotel Johor Bahru.
Following is from wikitravel.
Normal Singaporean taxis are not allowed to cross into Malaysia (and vice versa). Specially licensed Singaporean taxis permitted to go to a single point in JB can be booked by phone (Johor Taxi Service from Singapore, tel. +65-6296-7054, S$45 one way to fixed point in JB, Kotaraya), while Malaysian taxis (which can go anywhere in Malaysia) can be taken from Queen Street at premium rates, around S$35 to points in central JB. A combination ride from anywhere in Singapore to anywhere in Malaysia can also be arranged, but you'll need to swap cabs halfway through: this will cost S$40 and up, paid to the Singaporean driver. In the reverse direction towards Singapore, you can take taxis from Kotaraya to any point in central Singapore (S$30) or Changi Airport (S$40).
You can also opt to share taxis from Queen Street, which usually works out to around S$8 per person with four people (or pay S$32 for the whole car). The main advantage here is that you don't need to lug your stuff (or yourself) through Customs at both ends; you can just sit in the car.
The most expensive option is to take a limousine taxi specially licensed to take passengers from any point to any destination, but only a few are available and they charge a steep RM150 per trip. Advance booking is highly recommended, tel. +60-7599-1622.