While change the bathroom fixtures and tiling seems simple those elements account for more than 1/2 the cost of many bathrooms. You can estimate the cost to remodel your bathroom with this online calculator http://www.remodelormove.com/bathroom-remodelling. A budget of $2800 will be tough - it just depends on which fixtures you pick and who does the tile installation. Tile installaton will likely take several days maybe even a week depending on the design and type of tile. You may want to consider other materials like solid surface or engineered flooring that will be less expensive to install

The average bath renovation cost is 13K. You could do the project DIY with builder grade materials only, but you won't be able to afford labor or even mid grade materials with that budget. Leave the bath alone until you develop those DIY skills or save more money.