But some research is already going on  using engineered bamboo fiber as replacement of steel.I got some research findings by Architect Braine Brownell from American Institute of Architect  and  pasting below.

Testing has resumed in recent years at the Future Cities Laboratory (FCL) in Singapore, based this time on the use of woven-strand bamboo (WSB)—a composite material developed in southern China that resists moisture absorption, swelling, and decay from bacteria and fungi. Also used in flooring, WSB is made by slicing skinned bamboo stalks lengthwise into thin strands, which are carbonized and dipped into a vat of water-based adhesive before being either hot- or cold-pressed in molds. The resulting composite products exhibit three times the density of the natural bamboo.

Another material is a variant of continuous basalt fiber (CBF). Developed in 1923, CBF is made from the dense and abrasion-resistant igneous rock. By the 1960s, it had found use in a variety of applications in the U.S. and the former Soviet Union, according to the trade publication Composites World. CBF exhibits 2.5 times the strength-to-weight ratio of alloyed steel and 1.5 times that of glass fiber. Most importantly, it does not corrode like metal and, unlike glass fiber, it is not subject to deterioration from acids. CBF is also inherently fire-resistant and can be used with various composites, Composites World reports.

There is no alternative material as reinforcement for concrete cheaper than steel. Reinforcement material must have high elasticity modulus and strength, so only high tech materials such as carbon fibre can be used as a replacement for high performance. Bambu or any high tensile strength organic material can not be used because of decay. 

On the other hand, low performance options could be exist. Adding goat hair or tow or low quality fibres or scrap steel wire into concrete mixture can increase tensile strength of the concrete. And using arch or dome geometry can help to decrease tension stress zone overall the structure.

http://www.sciencedirect.com/science/article/pii/S1359836809002194

This article is not exact solution of your problem but it can be help you to understand phenomenon of enhancing tensile strength of concrete. 

But some research is already going on  using engineered bamboo fiber as replacement of steel.I got some research findings by Architect Braine Brownell from American Institute of Architect  and  pasting below.

Testing has resumed in recent years at the Future Cities Laboratory (FCL) in Singapore, based this time on the use of woven-strand bamboo (WSB)—a composite material developed in southern China that resists moisture absorption, swelling, and decay from bacteria and fungi. Also used in flooring, WSB is made by slicing skinned bamboo stalks lengthwise into thin strands, which are carbonized and dipped into a vat of water-based adhesive before being either hot- or cold-pressed in molds. The resulting composite products exhibit three times the density of the natural bamboo.

Another material is a variant of continuous basalt fiber (CBF). Developed in 1923, CBF is made from the dense and abrasion-resistant igneous rock. By the 1960s, it had found use in a variety of applications in the U.S. and the former Soviet Union, according to the trade publication Composites World. CBF exhibits 2.5 times the strength-to-weight ratio of alloyed steel and 1.5 times that of glass fiber. Most importantly, it does not corrode like metal and, unlike glass fiber, it is not subject to deterioration from acids. CBF is also inherently fire-resistant and can be used with various composites, Composites World reports.

To strengthen weak soils, here are links to some published works that used waste materials:

1. Steel slag -  https://www.researchgate.net/publication/269401452_Soil_Modification_by_the_Application_of_Steel_Slag_R_periodica_polytechnica_ci_Creative_Commons_Attribution

2. Marble fines - 

http://www.tandfonline.com/doi/abs/10.3846/16486897.2014.1002843

3. Corncob ash - 

https://www.researchgate.net/publication/271013861_Effect_of_Corncob_ash_on_the_geotechnical_properties_of_Lateritic_soil_stabilized_with_Portland_cement

4. Cactus mucilage - 

http://121.183.206.200:8080/proto.board/abstractArticleContentView?page=article&journal=gae&volume=8&num=5&ordernum=2&site=korsc

5. Reclaimed asphalt - 

https://www.researchgate.net/publication/263367831_Plasticity_Strength_and_Permeability_of_Reclaimed_Asphalt_Pavement_and_Lateritic_Soil_Blends

Article Soil Modification by the Application of Steel Slag (Ŕ period...

Article Effect of Corncob ash on the geotechnical properties of Late...

Article Plasticity, Strength and Permeability of Reclaimed Asphalt P...

CFRP (Carbon fiber reinforced polymer) can be used for this purpose

You can use bamboo.