Sorry I'm not sure I quite understand what you're suggesting - the 'deposit' is usually paid (or rather held on account by solicitors) at the point of exchange of contracts but before completion of sale, and is forfeited by the buyer if they fail to complete the contract. But you wouldn't be in a position to exchange contracts until you sell your house anyway from the sounds of things, so I don't see how a larger deposit changes things? It isn't unheard of although not common (in England/Wales anyway, Scotland has an entirely different system) to pay a small holding deposit after the offer but before exchange, to be forfeited if you don't get to exchange within a certain time period. But £70k is a huge amount of money to risk considering you've no way of knowing how long it will take to sell your house, whether your buyers once you have them will run into difficulties, whether issues will come up somewhere in the chain with surveys or mortgages causing the whole thing to collapse, and generally seems mad to risk that much money - the usual amount to offer pre-exchange just to show you are serious would be maybe £1k.
Personally assuming you are in England/Wales and you are desperate to get this particular bungalow, I'd get my house on the market attractively priced to sell pronto, then make an above the odds offer to the bungalow seller to reflect the fact there is uncertainty on your time scales. OR, depending on your financial position otherwise and the price of the bungalow, you might perhaps be able to take out a bridging mortgage to be able to own both at once for a short period, this will likely be expensive and perhaps not possible if you don't have a large income, also be wary of second home regulations etc, but could be a short term solution that is worthwhile if this bungalow really is a unique opportunity. Otherwise you might just have to accept that if this is a very desirable option you might get undercut by a cash buyer who is able to proceed quickly, this unfortunately just is how it goes when buying/selling, and there will be other houses out there.
I'd certainly try and do some digging/question the agent when you go to view about the sellers position, obviously they are going to try and create a sense of urgency to get the maximum price from you, that's their job at the end of the day but if you read between the lines you may get a sense of saying whether they are actually in a big rush or if they're prepared to wait if they achieve a higher price, would they be bothered about selling to a developer (which is common with bungalows) or would they be moved by the idea of someone who loves and will take care of the property as it is and be nice to the neighbours etc. If it's a probate sale they may actually appreciate someone operating on a slightly longer timeframe and/or who would offer to take care of some of the clearance etc, it's surprising sometimes what people's priorities are (I once managed to save what amounted to thousands on the purchase a house by saying the sellers (executors who lived abroad) could leave all the furniture and carpets etc in situ, I had to pay clearers a few hundreds to bin it all but still absolutely worthwhile and I guess worth it to the executors to not have to sort all that remotely?)